It’s not so much that they merged the games, but that non-Advanced D&D hadn’t been made for so many years, they figured that the A in the name was just worthless information.
Just for a brief rundown, in Tolkien, “wizard” is used to translate “istari”, which has a similar “wise” etymolygy, and used of Gandalf and his ilk. “Sorcery”, on the other hand, is black art, which can, potentially be used by anyone.
In D&D 3E, wizards are “book mages”, who use their intelligence to go through the arcane procedures outlined in their spellbooks, whereas sorcerers have inherent magical ability, shaped by their own force of will or personality.
In several computer/video games I’ve seen, a sorcerer specifically deals with flashy, unsubtle magic like fireballs and lightning bolts, which mostly just do damage, while a wizard is a more general term.
I believe that the Old Testiment differentiates between various sorts of wonder-working (most of which is forbidden), and the words “wizard” and “sorcerer” are sometimes used to translate the Hebrew words. For example, Pharoh’s “sorcerers” were able to replicate the staves-to-snakes “trick”, but Moses’ staff-snake ate their staff-snakes.
In some books (such as Brust’s Jhereg series), there exist sorcerers, but not wizards, or vice versa.
In some other books (Harry Potter, Xanth), there is no distinction made between the two, or other magical sorts such as magicians and witches.