Surface Integrals, Stokes Theorem, Divergence Theorem, all the same?

So am finishing up calc 3 and we are doing surface integrals, stokes' theorem, and divergence theorem.

But solving all the problems gets really confusing because I feel like all the different methods get mixed up. For example, in my book for the section on Stokes' theorem they might say evaluate using Stokes' Theorem but they will use the line integral method.

How do I know when I can use the method involving Curl F dS or F dr.

I know I am probably not providing enough info, but I hope you guys know what I mean.