HiBC has it right. Barrels and barrel making processes are not equal.
Cut rifling: Creates land profiles by removing metal from the reamed bore, one groove at a time. It does not introduce significant stresses into the steel, but it leaves toolmarks. This is how making the bore slightly undersized and lapping it became popular with custom barrel makers.
Button rifling: Swages the grooves into the bore using a carbide button to push into the steel. To make room for some of the displaced metal, the bores are usually slightly oversize to start, but seldom are touched by the button, so the reamer marks normally survive the process. In a bad barrel, this can result in off-center rifling, which I've seen twice in production barrels and which caused keyholing in both cases. It leaves very high outward radial compression stresses around the grooves which have to be relived by heating a rifled barrel blank to about 1100°F for about an hour in a non-oxidizing atmosphere. If that isn't done, contouring the blank usually results in the bore widening where the contour is thinnest, as the stress try to relive themselves. Mass manufacturers often do not relieve the stresses, so if you slug them from both ends, pushing the slugs through feels different, with resistance obvious going from the muzzle toward the breech, but almost none the other way as the bore is gradually widening. I have lapped the breech end of a number of less expensive brand Garand replacement barrels over the years. The almost uniformly were half a thousandth narrower from the lower band contour to the breech end where the contour is heavier. If the barrel is stress-relieved (Douglas does this, for example), then contouring has no impact on the bore's uniformity. It then keeps whatever uniformity the maker gave it.
Broach cut rifling. This is like a hybrid of the above two processes. The broach is a sort of Christmas tree of progressively taller teeth shaped like the groove pattern. It is pushed through like a broach and cuts all the grooves at once. This leaves less stress than button rifling but a bit more than cut rifling by single cutter, and the metal shavings can fail to flush perfectly, leaving longitudinal scratches in places. I'm not aware of anyone in the U.S. doing this currently, but there could be.
Hammer Forging. The barrel starts out as a tube and is hammered by multiple rotating hammers against a hard mandrel that looks a little like a bore casting with rifling shown in negative form, forging the lands to form down into the mandrel. This produces high stresses, but in the opposite direction from button rifling, so it doesn't tend to pull the bore diameter the wrong way. Also, contouring is mostly done during the hammering, so little steel needs removal anyway. Some even like to leave the hammer marks. I have only one such barrel on a gun (a Steyr) but it is very accurate and not bad to clean. I don't actually know if they need to stress-relieve these barrels or not.
In general, you'll find custom cut rifling that has been hand-lapped, as Gail McMillan did it, will see little benefit from any further sort or lapping or break-in, except a tiny bit in the throat cut after the lapping was done. Varmint Al says he runs a patch with Flitz about 50 strokes in such a barrel, and that is his break-in. Only if the barrel still fouls afterward does he repeat with JB and then Flitz again to get it a little smoother. To my mind the jury is out on how important the throat toolmarks are to address.
Lapping or firelapping barrels that are narrower at the breech end of the bore is almost always necessary for peak accuracy to be achieved with them, assuming the rest of the gun (action trued and lugs lapped if needed, and properly bedded) is up to top accuracy.
I feel like I am forever correcting people who suggest lapping is the same as wear from shooting and somehow uses up barrel life. That is flattly untrue and comes from not understanding the differences in the two mechanisms. Throat wear is due heat being unable to penetrate the bore surface steel more than a couple of thousandths of an inch during the time the bullet is in the barrel. This expands the bore surface especially near the throat because that is where the bullet base is when pressure and temperature peak. The steel below that surface (the substrate steel) is stressed by this where the expanded part interfaces with it. When the bullet clears the muzzle and the pressure is gone, the thermal transient front then expands out into the steel, but the stress caused by the initial temperature differential has weakened the grain boundaries in the steel just below the throat surface. This is what results in the alligator skin cracking pattern in a worn throat. Pieces of that skin start to break loose eventually, and that causes the throat to lose symmetry and the asymmetry is what messes up bullet balance during rifling impressing into the bullet. It does that irregularly, with the result the symptom of a shot out barrel is intermittent uncalled fliers that become more frequent as the wear progresses.
Lapping does not cut into lands any faster than it does grooves, so it introduces no asymmetry. The only exception to the cutting speed difference is during bullet entry at the throat due to impressing the rifling into the bullet with abrasive sandwiched in between, so the throat gets a slightly more gradual taper from firelapping. That doesn't hurt anything. Indeed, experimenters with extreme accuracy get reamers made with extra shallow throat angles, feeling the more gradual engraving will help keep the bullet better centered in the bore. But the bottom line with firelapping is it does move a throat forward a little. I have used the military type throat wear gauge on the Garand barrels I've firelapped and get about 1 to 1.5 thousandths increase in reading depth afterward, whereas the breech end of the bore itself is growing only half a thousandth in diameter.
Jack Belk, of Remington trigger law suit fame (his book, Unsafe by Design, is t Amazon and is well worth a read to better understand trigger mechanisms) said that while in the army he got the idea he wanted to remove the rifling from a bore to experiment with a smoothbore for some reason. He thought he could do it by lapping it enough. Nope. He worked at it a long time and the bore just gradually got bigger but still had rifling.
G. David Tubb actually takes advantage of the extra throat lapping during bullet engraving to lap away irregular spots in damaged throats with his Final Finish version of firelapping. He claims he has recovered the accuracy of guns with shot out throats and doubled their accuracy life this way. He uses jacketed bullets and full starting loads, which increases the action of that land engraving lapping on the throat.
The bottom line is that wear from shooting tends toward throat asymmetry and lapping tend toward throat symmetry. This is a vitally important distinction.
The objection was made to lapping rounding edges on rifling. I wish it would. According to Boots Obermeyer, part of the whole secret to the long life of 5R rifling (and yes, Mike Rock is the fellow he taught who then underbid him) is that the sides of each land are sloped rather than sharp, and some of the chrome-moly military barrels with this rifling have gone over 10,000 rounds, which is about three times the normal life of a chrome-moly steel .308 barrel. Why the throat is holding up so much longer is probably explained by that contour eliminating the weakest, most vulnerable edge in the rifling, the outside corners of the lands, which get the hottest in the throat and are the weakest part of the standard rifling profile and therefore are the most easily damaged by heat stress. But lapping will dull a land only to the extent of the size of the lapping particles. Rifling gets lapped a little bigger in diameter as a whole, but military specs for .30 call service rifle barrels is .3065"—.3095" for the grooves and 0.2985"-0.3015" for the bore. British competitors used to prefer a .309" groove rifles, claiming to find them more accurate by letting bullets bump up to fill them. I'm thinking they may still have been greasing bullets at the time, so don't read too much into it, but do know that unlike cast bullets, jacketed bullets can expand a little during firing without gas cutting or other balance problems occurring. Besides, many match bullets are actually about half a thousandth oversized the widest place, so you would have some wiggle room there even if they didn't upset to fill a bore under pressure. The point is, the bore being uniform and/or tapering slightly narrower toward the muzzle is preferable to being uneven or tapering wider toward the muzzle. So the slight widening at the breech end isn't necessarily undesireable.
When NECO developed the firelapping process originally, they got the University of San Francisco rifle team to allow them to firelap 27 of their .22 rimfire rifles. They averaged a 15% reduction in group size, with none getting worse. From NECO's description:
NECO said:
There have been numerous third-party civilian and military tests of our process, with reported results similar to our own. At least one International Palma team which now regularly laps its barrels with our kits has reported a tenfold increase in the number of shots which can be fired accurately between cleanings, from 20 to 200. Attainable accuracy improvement is dependent upon the overall condition of the firearm, but spectacular improvements are frequently obtained in rifles, including military weapons such as the M1 Garand, and the process is very rewarding in revolvers. There have been varying results, but none negative, with autoloading pistols.
Some of the custom barrel makers say you don't want to make the surface too smooth or fouling will actually be worse. This does not match my experience, nor, apparently, Varmint Al's. The NECO kit goes down to 1200 grit. When firelapping Garand barrels, I counted the number of patches need to get the bore clean and free of copper (turning the patch blue) after every five lapping rounds. It kept getting progressively fewer all the way through the 1200 grit lapping bullet firing, by which time it was taking about six times fewer patches. This is in line with the claim made by the Palma team, above.
One of the reasons firelapping has gotten a bad name in some quarters is that after NECO patented it, Wheeler Engineering decided to ignore the patent and copy the idea; but only approximately. The cost of defending the patent was prohibitive for a small company (about the cost of a house to take it to court, typically), so NECO never did. Then other copycats jumped on board. The problem was that Wheeler copied NECO's abrasive grades but ignored a key factor: the NECO abrasives are laboratory grade. Standard commercial lapping compounds like Wheeler used have a much wider range of particle sizes. This not only makes them cut about half as fast (this from astronomical mirror makers; its due to too much sub-grade size particles packing around the coarser ones and clogging the cutting action), but in the coarsest size used, 220 grit, the largest particles in standard grade compounds are big enough to put some serious gouges in steel. So a number of people with the Wheeler and other copycat kits wound up damaging barrels by the combination of making those scoring scratches and having to shoot more rounds to get the job done. If you are going to use commercial abrasive grades, don't go coarser than 320 grit and be prepared to take 50 shots to get as far as the NECO kit does in 10 to 20).