Or is it Corey Perry you are thinking about? Carter is close in that regards though.
i was just saying that of the championships that you listed, carter has all the same ones as richards, because they apparently are joined at the hip.
one championship richards has but carter doesn't, however, is the memorial cup, which you did not list.
ftr,
mike richards: memorial cup, WJC gold, calder cup, olympic gold, stanley cup
jeff carter: WJC gold, calder cup, stanley cup, olympic gold
corey perry: WJC gold, memorial cup, stanley cup, olympic gold, world championships gold, world cup gold
scott niedermayer: WJC gold, memorial cup, stanley cup, olympic gold, world championship gold, world cup gold
joe sakic: WJC gold, world championships gold, stanley cup, olympic gold, world cup gold
jarome iginla: memorial cup, WJC gold, world championships gold, olympic gold, world cup gold
back on topic, a famous example of a guy who won the calder cup and stanley cup, albeit in back to back seasons not the same year, was patrick roy.
as for the real question, one guy played playoff games for both the calder cup-winning '95 albany river rats and the devils of the same year. his name is kevin dean and he was the captain of the river rats.
pierre mondou, brian engblom, and mike polich all played playoff games on both the calder cup-winning '77 nova scotia voyageurs, which was a shared AHL affiliate between the flames and habs, and the '77 habs.