Actually, tetris battle pitts you against replays of other people's games, unless you actually challenge another player. Even then it's not 100%... A friend of mine once challenged me and ended up playing a replay. (Actually, he let me play myself. I lost. )= )

I'm not sure how they handle bombs, since certain moves only make sense given bomb timing and positioning. Also not sure how they handle moves that become impossible at the very top of the screen -- if line timings are different, the replay ends up trying move to a place that a real player actually can't get to.

Edit/Note: If you're playing someone live, it'll say so under your names -- one of you will have 'host' and the other 'live.'