24, 25, 30, 60p are all frames/second, right? Ok, so wich is the final dirrefence?
I'm not quite sure what you mean by "the final difference" (or 'dirrefence,' I like the sound of that

)
Is there a real difference between 24 and 25p??
Yup.
24p is the classic movie frame rate used for decades all over the world. It predates TV and video. It was used with analog films and mechanical film cameras, and it's still in use even in most digitally made movies. Although these days the actual digital/electronic frame capture rate may be slightly under 24 frames per second in some cases/regions, but that's another (long) story for another thread.
25p is the TV standard used in most of the world, except in North America. It's close to 24p, obviously, but for different reasons. The frequency of the power grid is 50Hz in these regions, so it makes sense to use a TV/video frame rate that is harmonic to that frequency to avoid flickering. So they use 25 and 50 fps. Very close to the 24p movie frame rate, but not at all the same thing. In short, 25p = TV/video, 24p = movies.
That's the quick, non-pedantic layman's explanation, anyway. You can study all the related details in Vikipedia or wherever you wish. There's plenty of more stuff about frame rates out there.
My camera is capable of 30 and 60p. 30 is classic speed, right?
Nope.
30fps is the frame rate the 'Murry Khans' (les Américains) and the Canoe People of the North are using. The rest of the world is using 25 and 50. 30p = North American TV (60Hz power grid).
Using 30p when shooting in the 25p region like Europe may lead to ugly looking footage where electric lights are either flickering or there will be a visible banding effect in indoor scenes shot in artificial light, or both. Depending on the shutter speed you're using. It works the other way around in the 60Hz land of the Murry Khans, too.
If you wish to make sure your video has no flickering or banding, you ought to use 25p or 50p in Europe. Preferably with a 180 degree (harmonic) shutter angle. (eg. 25p -> 1/50, 50p -> 1/100)
60p let me do slow motion? or this is 24p?
50/60p lets you do slow motion, too. Sort of.
So, how does it work slow motion capture? With my camera (30p and 60p) can I do it? Is there a parametre I have to change in my camera or is something else?
You can shoot your video clips in 60p and then slow the footage down in your editing app like Premiere, FCP and so on. That's the simplest way. Try it yourself and see how it looks.