I know that there is a two types of animations… I don’t know actually the names of it, but I’ll try to explain.
1-st type is playing animation on one place. It’s like character play walking animation but don’t actually move.
2-nd type is playing animation like in real life. Character play walking animation and move forward.
So question is, which animation should I use in Unity game?
For games like Assassin’s creed or GTA 4,5.
P.S. Sorry for bad English )
It’s not clear from the question exactly what you need help with although, without any doubt, your English is better than my version of your first language!
I think you might mean Mecanim and legacy. If so then you can use either or even both.
In my experience Mecanim is worth using for it’s ability to use the same animation on many different humaniod characters.
On the other hand the legacy system allows for some things that are difficult or impossible with Mecanim like playing an animation backwards.
None of this is a problem as you can use both if you need to.
Just because you can re-target animations with Mecanim I’d use that, it’s worth learning and there are plenty of Mecanim tutorials on Youtube.
Just be warned though that a lot of characters with built in animations will be legacy, again not a problem as you can swap from one format to another (for humanoid rigged characters anyway).
Also note if you bring in a character you will need to duplicate the animation as they appear to always import in read only format.
Good luck.