The question stems themselves differ in the following way:
Necessary premise - will ask for an assumption that is in some way needed, required, argument depends on, etc. (uses necessary indicators)
Sufficient premise - will ask for an assumption that, IF provided, would allow the argument to be properly draw, fully justified, prove the conclusion, etc. (Uses sufficient indicators; primarily if)
For strengthen with necessary premise, you should be looking for an answer choice that the argument really requires in order to be true. While for strengthen with sufficient premise, you should be looking for an answer choice that would guarantee the truth of the argument.
I hope this helps. Please let me know if you have any questions.