Well, first of anything a war game completely different from a strategy game. Both are completely different genres.
War games are games like
Battle Isle and
Fields of Glory in which the gameplay is restricted to controling every single units on a board and you need to find the right strategy to win against the pieces of the opponent, which are usually already set up. This kind of game focuss entirely on the battles and the units themselves and can often be compared to a game of chess.
Strategy games are games like
Civilization,
Master of Orion and the like, in which you might or not control all single units like war games, but the game is completely centered on you building and defending an empire first of all. This kind of game is centered on management and overall strategy over a long time.
Then, you can also have a third kind of commonly known strategy game, which are called RTS for Real Time Strategy. Those games will look like
Command & Conquer and are centered on action and reflexes. There is very little strategy in RTS, except for those old gems which play at slower speed.
Some people consider war games to be a subclass of strategy games. In such a categorization, games like Civ and MOO become what is known as 4X games (which is short for "eXplore, eXpand, eXploit and eXterminate").