WoW has you playing online all the time (you can not play offline) in a persistant world with hundreds of other people.
You control one character alone in WoW - you tend to control groups of units in an RTS. World of Warcraft is a MMORPG (Massively Multiplayer On-line Role Playing Game) while Warcraft 3 is a RTS (Real Time Strategy). They take place in the same world and as such have the same background/lore to them but that's about the limit of the similarities.
World of Warcraft and Warcraft 3 are completely different games.
