discrete vs continuous synchronization

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Hello, fellas
I have few questions, maybe my questions doesn't even make a sense, I'm a newbie, take it easy on me ^_^

FPS style game or 3rd Person
For bullets detection would be better to use continuous collision detection? Or it's not even possible

And what about difference(in data usage) we actually talking, like using it for animation/bullet synchronization(discrete and continuous), about few cent's per user of month usage ? because if player moves like in photos slideshow it would make game look cheap, or some bullets just flies throw the other player undetected

Feels like I'm missing something about bullets and their synchronization over the network

I'm just finishing Basic Tutorial, so maybe I will find my answers in documentation which I started reading a while ago