Is there links between the different opus of Far Cry ? I wonder why the one was with mutants and the others more realistic with only humans

Nope. Just like there's no connection with the Quake games (except I think 2 and 4).

They just used the name to get more sales.

There's a theory (which I subscribe to) that Jack in fc1 is Jackal in fc2.

There is only one link: Ubisoft acquired the IP and they can make any number of far crys and assassins creeds and so on. Nothing but a little business exploitation.

There is indeed no solid link between 1st and later iterations (although this Jack is Jackal theory looks rather attractive indeed). 2nd through 4th, however, are seem to be interconnected: the weapon dealer from 4th appears to be one of warlords from UAC; Willis from 3rd makes brief appearance in 4th.
I wouldn't call 3rd and 4th games of the series realistic. As in Brock Samson's Simulator unrealistic (especially considering backgrounds of the protagonists).
Far Cry 2, though, gives me a bit of that good Arulco vibe.