AR rifles are generally 20" barreled, and commonly have fixed stocks. AR carbines are generally 16" barreled, and commonly are copies of the M4, with adjustable stocks.
Gas length on them all is where the front sight block, or FSB is located, which times the action to open the bolt properly. That means about 5-7 inches from the muzzle to get the optimum timing.
Originally, carbine gas on military issue M4's and others was based on the issue 14.5" or shorter barrels. But, the BATF does not allow possession of barrels under 16" without a special Short Barrel tax paid up front. That tends to put a crimp in impulse sales and overall demand. To supply that, AR15 assemblers used 16" barrels, but the carbine gas tube and handguards. That left a lot of barrel after the gas block, opened the bolt early under much higher pressure, and caused a lot of head scratching in Customer Service departments and the design engineers offices wondering why Marketing created an expensive problem. The bolts were failing much earlier, more often, kabooms were getting reported a lot more on something called the internet, which seemed to let people communicate a lot more quickly about problems.
They invented midlength gas, and in the process, had to justify the expense of midlength handguards, which weren't miiltary issue. The tooling costs were appparently worth it, because midlength gas guns, with the gas block where it should be on a legal 16" barrel, became the civilian standard.
If you want to decipher what a particular AR is meant to do, it's really no different than other guns. Actually easier, the differences are more obvious because thats all that gets changed. Other guns makes taken as a whole confuse it by hiding things in different designs.
IN GENERAL, some broad definitions: long barrels for long range, short barrels for short range. Fixed stocks for hunting or precision shooting, short adjustable stocks because the shooter is wearing heavy clothing or an an armored vest on occasion. 5.56 for competition, cheap shooting, or large quantity shooting, alternate calibers for the higher power and/or longer range they offer.
Examples: 20" flattop fixed stock AR, general purpose use. Add a precision barrel, free floattube, bipod, and 4x12 scope, it's a varmint gun or long range precision shooter. Put a 16" barrel with handguards, in 6.8SPC, with a red dot, it's a deer rifle. Swap an adjustable stock, eave the red dot, 14.5" barrel, and add a suppressor, it's an LEO trunk or call out team carbine.
Leave the 14.5" barrel, pin a long flash hider to make it 16", add the 4x12 and bipod, and yes, it gets very confusing. A 50m precision hostage taker gun, maybe, in metros with an antiterrorist need. Or, just a screwed up gun because it seems so macho somebody had to post a picture of it. Happens all the time, it's practically a cliche. Just add lasers and a 6 C cell maglite.
When you are ready to buy, or build, know what targets at what distance you'll commonly be shooting at. That tells you the caliber and barrel length, then choose the better stock, grip, handguard, optic, flash hider, and last, trigger. In that order, based on What target at what range, you get the optimum combination you need for the job. It's not always what seems cool, but shooting it will be successful with fewer mistakes, and that IS cool.