Refuse vs. rebuff

rebuff
verb [ T ] UK ? /r?'b?f/ US ? /r?'b?f/ formal
?
to refuse to accept a helpful suggestion or offer from someone, often by answering in an unfriendly way:
She rebuffed all suggestions that she should resign.

Could anyone explain the difference between 'rebuff' and 'refuse'? I feel rebuff is more more formal, and refuse is neutral without being impolite or unfriendly. Thanks!