Magic User was renamed "Mage", and groups of classes with similar abilities were grouped together.
WARRIOR: Fighter, Paladin, Ranger (d10 HD, 1:1 Thac0, multiple atks)
PRIEST: Cleric, Specialty Priest, Druid (d8 HD, 2:3 Thac0, Divine Spells)
WIZARD: Mage, Specialist (Illusionist et all) (d4 HD, 1:3 Thac0, Arcane spells)
ROGUE: Thief, Bard (complete change from 1e) (d6 HD, 1:2 Thac0, % thief skills (8 thief, 4 bard)
In addition, class groups used the same saving throw tables, WP/NWP rates, and XP charts (though Druid, Paladin and Ranger used a second column of those tables)
Psionics was regulated from the core to the Complete Psionic's Handbook. It was revised again in the Will and Way (Dark Sun) and PO: Skills and Powers
Barbarian was reprinted in Complete Barbarian's Handbook (and as a kit in Complete Fighters)
Cavalier became a kit in Compete Fighters
Monk became a lame Kit in Complete Priests, a spellcasting class in PO: Spells and Magic, and the martial arts class again in Scarlet Brotherhood
Assassin became a kit in Complete Thieves before returning to class status in Scarlet Brotherhood
Thief-Acrobat became a kit in Complete Thieves
Half-Orcs and Half-Ogres recieved PC write ups (though really wonky ones) in the Monster Manual, and proper one in Complete Book of Humanoids and again in PO: Skills and Powers.
Ninja got its own class in the Complete Ninja's Handbook, the last Complete Book to come out.