While there are as many variations as collectors, and of course there's a lot of overlap, there are basically two different kinds of collectors.
Those that was a certain, specific gun, as original in all aspects as possible, and willing to pay to get it.
Then there are the others, myself included, who just want some shootable example of the gun(s) we are interested in. And we're willing to have wear, poor finish, mis numbered parts, reblue or about anything else as long as the gun is mechanically sound, and not pay top dollar for it.
Examples abound of what are technically "fakes" or "repro" in certain guns, and no harm is done at all, provided they aren't made out to be something they're not.
I always wanted a Luger P.08 Found a 1936 s/42 that looked brand new. one mismatched part (sideplate, of course) wrong (aftermarket) grips, but looked brand new. Story with it was "it was refinished during the war",, but one buys the gun, NEVER the story, unless there is certain documentation included. Anyway, the seller didn't try to claim all original, sold it for $750. Had it been all original it would have been $2200 (at that time). Good deal for me, got a pristine looking Luger, I could shoot without risking its market value, and that's what I wanted.
Another guy would sneer, and pay $2200 for a beat up one that was "all original".
Some guns are worth more as rusted hulks of post battle debris than the same gun refinished to look new. The collector is paying for the HISTORY more than the gun.
A friend of mine wanted a Winchester made M1 Garand. Couldn't find one completely Win at any price he was willing to pay. Bought a Winchester M1 that was a mix of parts, and spent a year or three tracking down and getting Winchester made parts to replace those others on his gun. Wound up with an all Win gun, but never claimed it was all original.
With US military arms, there are two different and historically correct versions. Those intact as originally issued, with all the original parts from the original maker(s) and those as found "in service" with mixes of parts, because that's what we did. We (servicemen, including repairmen) never tracked individual parts by maker or anything else. We didn't ser# parts like Germany and some others did. Some of our guns were never assembled from parts of a single maker.
A 1911A1 with all Colt made parts is historically correct. For a certain time period, it is the only historically correct version. In a different year, a 1911A1 with a Colt frame, Ithaca or Remington slide, and small parts from half a dozen different makers is ALSO correct. Each one has a different value to the collector, depending on what the collector values most.
I once had a Broomhandle Mauser, the Bolo variant. Originally .30 Mauser, made in the 1920s. When I got it, it looked new, and had been bored to 9mm Luger. Worked fine, looked good and was worth about half what a beat to crap but never reworked one was. And about of quarter of what the really rare new looking original brought.
Ok, I buy the cheap stuff "real" collectors don't. But they work for me, and give me a chance to own and learn guns I'd never be able to afford otherwise...AND, I've never lost even a penny on any of them that I later sold off.
Actually having and shooting a gun teaches you things reading about them never can.
Nobody ever seems to mention that the Walther P.38 ejects to the LEFT!!!
Or that shooting a 9mm C-96 Bolo without the stock is PAINFUL unless you wear a glove!
or, as a little known tidbit, that you can cock an M1 Garand or M14 without working the bolt!!
(no idea why you ever would, but you CAN do it,)
Also having one for your own is better than just seeing one on Utube.