In addition to what has been said already, I would say that "remporter" mainly means "gagner une victoire". So there are no many words that can be object of the verb "remporter" as you can see in the link below: http://corpus.leeds.ac.uk/cgi-bin/cqp.pl?q=remp...
bur "gagner" has a lot of meanings:
You can say:
- gagner la confiance de quelqu'un BUT NOT *remporter la confiance de qqn)
- gagner sa vie BUT NOT *remporter sa vie
- avant le spectacle, je sens le trac me gagner (NOT *me remporter)