Yep, completely different games even though both came out in spring 2004. Different developers, different publishers. Red Dead Revolver never came to Windows, Dead Man's Hand never went to PS2. Both had xbox port though.
Dead Man's Hand doesn't deserve much praise as it was quite bad budget game. It's only importance was that it was one of few wild west FPSes in first half of 00's. Before that came only (also budget title) Western Outlaw: Wanted Dead or Alive in 2003.
Of course, there were also even more obscure wild west shooters, but those weren't pure FPSes. Like Swedish "Wanted Guns" in 2003 and Polish "Gun Warrior" in 2005 (by Frontline Studios).
But one can think that lack of good wild west games on market since 1997 Outlaw was reason why GUN and Call of Juarez series were born.