TC, you can buy d3 or expac digitially through blizzard online store or find it at boxed copy at a retail store. Blizzard games don't on sale digitally very much, maybe like once a year or so for a special occaision usually. If you want on sale, best bet is to watch the prices at places that sell the boxed copies.
Anyways, no matter what version you buy youll have to download the battlenet client which is kinda like steam, but its only for blizzard games. You can download and launch and patch all blizzard games through the client such WoW, Diablo 3, StarCraft 2, Hearthstone, etc.
Battle.net is basically Blizzards equivalent of Uplay or Origin. They only sell there own games on there service. Steam on the other hand is more comparable to XBL or PSN except with amazing prices and sales.
Everything EA contributed to gamers around the world in one youtube clip http://www.youtube.com/watch?v=kBoesEFWZnM