Yes, it's different from the nirvana fallacy. The nirvana fallacy is: "X is the ideal perfect goal; Y is a proposed solution that fails to completely achieve X; therefore Y is not worth doing." e.g. "World peace would be ideal; this peace treaty fails to completely achieve world peace; therefore this peace treaty is not worth doing."
The fallacy you call "appeal to futility" is, "X is the ideal perfect goal; there is no possible perfect solution Y that completely achieves X; therefore X is not worth attempting." e.g. "World peace would be ideal; there is no conceivable peace treaty or other action that would completely achieve world peace; therefore, there's no point in working towards world peace."
It's fallacious, yes. Although a goal may not be achieved fully, there can still be value in striving for it, because the effects of doing so are good. For a simple example, when we shoot arrows on a range we aim for the perfect center of the target. We're never going to hit the absolute perfect center, which is a point of 0 size, but trying to hit the perfect center helps us to get closer to it and shoot more accurately.