In Deadlands Classic, cards are used for character generation and for initiative (Action Cards), as well as gambling, spellcasting (hucksters), and inventions (mad scientists). Chips are used as fate chips.
In Deadlands Reloaded (Savage Worlds rules), cards are used for initiative (just as in normal Savage Worlds) and chips are used as fate chips as a Classic-like modded variation on the usual SW bennies. Cards are also used for dueling, gambling, spellcasting (hucksters), and Harrowed abilites but not Mad Science/gizmos. This version runs a lot like Classic, really, slightly simplified.
In Deadlands d20, there are fate chips but the role of cards is much reduced - magic uses spell points/skill rolls, initiative is d20 style - I'm not sure if there's a use for playing cards in any of the expansions, but cards are not part of the core game at all. Warning: d20 Deadlands is in general a poorly regarded conversion attempt.
I don't have GURPS Deadlands: Weird West, but I am given to understand it uses cards some (for hexes) but not as pervasively (not for chargen, initiative) and does not have Fate Chips. (Of course, grafting Fate Chips back on is trivial and many folks have done that when playing GURPS: Deadlands.)