I'll put it in bullet points
1. Combat is much slower, but at the same time feels a lot more smooth (BFA has global cooldowns on each ability, while BFA combat is much faster and much easier since enemies die so fast, it far less smooth feeling due to GCD).
a. Low level paladins expect to auto attack...a lot...gets a bit better later though
2. Far grindier. For one example...like a true oldschool RPG, if you want to switch from (for example) one handed hammers to two handed hammers, gotta grind up the skill by actually using it. Same if switch from hammers to swords
3. Talent trees are far more indepth. And just like BFA, you can choose the optimal path or choose your own path, except in vanilla the path has a lot more choices
4. Crafting is far more useful. Blizzard has over time made crafting less needed. In BFA by the time you can craft the good crafted stuff, you'll already have better items from dungeons and even quests
5. Very few race choices. This will hit many, because there are no blood elves, worgens, goblins or any of the other races. Just the 4 basic race choices for both factions.
6. gotta buy abilities, you don't auto learn them
7. Money is super hard to get. I was always bad at money even in Legion and it was far easier to be rich in legion than vanilla
a. don't expect to be able to afford your mount of you play "normally" by just following quests and occasional dungeons
b. don't expect to be able to afford all your abilities since gotta buy them and starting out you gonna be poor poor poor
c. no mounts for a long time, if you can even afford the mount
8. speaking of mounts...no flying mounts. the mass amount of people that whine about flying every expansion won't like classic AT ALL. cause they'll have to run everywhere until they are both at right level for a mount and have enough money...and they still won't be able to fly
9. Soloing is possible, but obviously not to the extent it was when WOTLK started with DKs
10. Shamans are actually good
11. Gotta do class quests (for some classes) to earn some of the special abilities or some special rare items (like paladins at level 20 get an unique hammer. Shamans need to quest for their totems)
12. barrens chat
a. barrens chat
b. barrens chat
d. barrens chat
13. Some class specs aren't gonna be wanted in groups like how shamans are the worst class in BFA. Like...ret paladins you'll be laughed at out of the game. And if you don't quit out of the game as a ret paladin, you'll be harassed nonstop until you quit. Luckily blizzard takes harassment and real life threats seriously so this should be a non issue compared to the free server that is available.
14. No shamans for alliance, no paladins for horde
15. Hey hunters! you are actually really hunters again. Carry that ammo, feed that pet, take care of that pet or it will leave you.
16. expect to die a lot if you solo. I actually died in the human starting area cause I got the attention of too many bandits by accident.
Feel free to add more. I probably missed a bunch of stuff