Dieter: We say here that equivalence is an important aspect of miai, whereas we also make equivalence an alias for miai.
Moreover, I'm missing the dynamic nature. I've been told that two moves are not miai, but that you can turn a position into miai, i.e. by playing moves that leave immediately equivalent options (for your own stones), reducing the temperature of that position.
Bill: The page currently needs some more examples. Especially since the one given is sente. If White plays on one of the miai points as reverse sente, we do not expect Black to grab the other.