I came across this information about differences between the two. I understand the future and not happened yet time example but what of examples for the other uses?
Gerunds are often used when actions are real, concrete, or completed.
For example: I stopped smoking.
(The smoking was real and happened until I stopped.)
Infinitives are often used when actions are unreal, abstract, or future.
For example: I stopped to smoke.
(I was doing something else, and I stopped; the smoking had not happened yet.)
This info comes from:
http://web2.uvcs.uvic.ca/elc/studyzone/410/grammar/gerinf.htm