These are some very general comments and ideas about these two words:
Impulsive tends to imply that the person is acting without control, that he/she can't stop from doing whatever it is. It comes from the word "impulse", which in this case could be a sudden burst of energy, desire, emotion, anger, etc. It often (although not always) has a more negative connotation. Example:
- My son's impulsive behavior is getting him into trouble at school.
Spontaneous is very similar, but it carries more the idea of doing something without planning it, and usually has a more positive connotation:
- We made a spontaneous decision to go to the beach for the weekend.
Compare these two sentences:
- He impulsively turned and kissed her. (To me, this means he couldn't control himself, even if he wanted to.)
- He spontaneously turned and kissed her. (This time, he wanted to and he did it without stopping to think.)
Other people will probably have other ideas, but I hope this helps!