Someone more qualified than me will provide a detailed explanation, with aspect ratios and other scientific principles. But I'll give you the gist of it from my experience.
Wave kites are designed to drift, so that when you are surfing a wave, even moving directly at the kite, they will just sit there and wait for instructions. The goal is to surf the wave with minimal kite input, closest to actual surfing -- then at the end of the wave you re-engage the kite and zip out for another. Wave kites are generally stable and forgiving, so that when you're surfing a wave and things go wrong, you have a better chance of pulling it off (this also makes them good beginner kites, also good for foiling). They usually sit back in the window (low aspect).
These benefits come at the cost of less better at jumping and other high performance aspects. A freestyle kite will maximize jumping and explosive power, but at the cost of not drifting as well.
A freeride kite is in the middle, a hybrid of both. And like all hybrids it can be either the best of both worlds or it does neither task well, depending on how you look at it.
That's how I see it ... now I await correction from the masses.