The difference between the two is that a Crab is done to overcome a crosswind (as was already mentioned)

A slip is done regardless of wind conditions, and is used to bleed off excessive speed when landing (Or otherwise rapidly losing altitude).

So for example:

If you are landing in a crosswind, you may need to Crab into the wind to stay lined up with the runway - or - If you are flying from point "A" to point "B" in a crosswind, you'll need to Crab into the wind to stay on course.

Whereas, if you start your final approach too high, you may want to side-slip the plane to keep from gaining too much speed as you decend.