People mix these up, then overpay. Sellers mix them up on purpose.
I have already written the Adidas player-issue breakdown. This is the wider version, because the same confusion hits Nike, Puma and the rest.
Stadium/replica. The shop shirt. Cheapest, loosest fit, the one most people actually wear. Nothing wrong with it if that is what you think you are buying. These usually have a thicker fabric than the higher-quality shirts and embroidered logos.
Authentic / “player spec”. Same design, better fabric, closer to what is on the pitch. Clubs and Adidas sell these as authentic. They are not player issue. Badges are often heat-printed to look like the real thing. A lot of listings price them as if a player wore them. They did not.
Player issue. Made in small runs for the squad. On modern Adidas, that usually means numbered sizes up to 2024 (2–13), not S/M/L, a tighter fit, and everything printed, not embroidered. I take a large in a normal Adidas shirt and a 7 in player sizing. These are the shirts the players wear. They do still have tags on, and on Adidas a different code in the neck. In Nike shirts, they have a printed wash label and a small code label (roughly 2020 onwards).
Match prepared / match issue. A player-issue shirt that was actually set up for a game: correct nameset, patches, sleeve sponsor for that match. People buy blanks and print them up. A Ronaldo nameset does not make it the shirt from the final. Check the size against other shirts from that player that season, and check the patches against a photo from the game. Provenance is key here.
Match worn. The one that was on the pitch. Different thing again, and the fakes at this level are better because the money is better. I personally avoid Beckett’s authentication like the plague, and Messi has been exclusive to Icons for years, so be careful with “signed, authenticated” shirts doing the rounds.
If a listing says authentic and the price is player-issue money, ask which one they mean. If they cannot tell you, do not buy it.
Shop match-worn and player-issue from me here when they are in. Everything else in the shop is checked as authentic under the guarantee.