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Two very closely related questions:
If a card has two different "Sacrifice this creature for X" abilities on it, does sacrificing it give both benefits?
Likewise, if a card requires a creature to be sacrificed, but that creature has a "Sacrifice this creature for X" ability, do you get the sacrifice benefit when you sacrifice it for the other requirement?
No to both - each ability has an individual cost, which you'll need to fulfill before it is put on the stack.
Anytime you see Sacrifice [X]: Do [Y], that is expressing a cost that must be paid in order to activate the ability. A single paid cost may not activate multiple abilities; see the following (from the comp. rules):
117.10. Each payment of a cost applies to only one spell, ability, or effect. For example, a player can't sacrifice just one creature to activate the activated abilities of two permanents that each require sacrificing a creature as a cost. Also, the resolution of a spell or ability doesn't pay another spell or ability's cost, even if part of its effect is doing the same thing the other cost asks for.
No, for the reasons given by Ian, however, if the card had read "Whenever a creature is sacrificed do X. Sacrifice a creature: Do Y" you would get both effects as the first is triggering to the action of sacrificing, and is not stating a cost.
