There are many differences in detail, which can be pretty significant or pretty negligible. For instance, there is the business with Priests and Spheres. We had (chiefly as the DM's fault) a player who did not understand, and kept playing his Cleric as if he had access to (and preference for) the Druid's spells in addition to what he ought to have had.
So, we had him turn instead to the 1st ed. PHB, with its separate Cleric and Druid lists.
Since most of the players have that handbook (only the DM having 2nd. ed. books), it ended up becoming standard.
Then, the DM wanted to look up prices for some magic items, and borrowed the 1st ed. DMG. That book is chock full of weird and wonderful stuff! When people stumbling over THAC0 was holding up the game, we turned to the tables of pre-calculated "to hit" numbers.
Those tables, by the way, have six repeating 20s before going to 21. Without that in 2nd, does a "natural" 20 always hit?
That's one of the more minor details. An AC works basically the same way! So do hit dice, levels, saving throws, movement rates, experience points and classes (although assassins and monks might be mysterious if you have only a 2nd ed. PHB, and bards are quite different). Psionics are very different in AD&D 2. The real basics are pretty much the same among Original, AD&D 1, the several Basics, and AD&D 2.
As I recall, the biggest difference between AD&D 2 and all the rest is that XP for treasure, although mentioned as an "option", is not the standard. That, and the level limits on non-humans are higher (whereas humans are limited to 20th).
Initiative and surprise use different dice and methods (both d6 in AD&D 1), and I think so do some other things. Weapon vs. armor is different. Druids and rangers are different. Rangers get 2d8 HD at 1st, 1d8 at later levels, and get druid and magic-user spells, in AD&D 1. Druids advance more (perhaps sometimes slightly too) rapidly in 1st edition. The AD&D 2 Rogue has basically the same features as the AD&D 1 Thief, but the numbers are different.
In 1st ed., "Wizard" is the title of a magic-user of level 11+. Each class has its own peculiar titles by level, so a party might be made up of a Champion, a Chevalier, a Pathfinder, a Lama, and a Warlock.
In 1st ed., elven fighter/thieves can cast spells in all sorts of armor.
Boy, I dunno. Seems one is likely to find something every few pages!