I know one implies the thing I'm comparing actually is the thing I'm comparing it to, and the other doesn't.
Can someone suggest an easy example or trick for remembering which is which?
～にしては means "Considering X is Y, ..."
～としては mean "As a / In the capacity of X, ..."
So the latter is when the thing actually is the thing you're comparing to.
Just adding to an existing answer because I typically don't think of these two as comparisons, I look at it from a different angle than the OP.
I typically think of this as more of expectation rather than comparison for ～にしては, although comparison could be valid as well but I never think of it like that.
So as @istrasci pointed out, ～にしては means "Considering X is Y...". There is an expectation involved because it typically goes against what the speaker is expecting from X.
From @istrasci's example, we have
Normally we usually expect rich people to lead a luxurious life, but in this case, Tom does not lead a luxurious life, therefore it goes against an expectation. So it is used to contrast a reality (does not live a luxurious life style) to some kind of expectation (rich people typically live in luxurious life style)
This is another example of contrast between reality (you were a first time skier and you were pretty good), to an expectation (first time skiers are not good)
For me ～として implies and empathize some kind of position.
Lawyer is a position being empathized here.
Student is a position being empathized here, I don't just want to apply, I want empathize that I want to apply as a Student.