[bold]‘cup tie’, meaning a competition with a cup as the reward for the winner[/bold]
dxb, I don't quote agree with this meaning, I'm afraid.
I think a 'tie' in the context you mean is one contest between two teams, rather than the whole competition, which is made up of a collection of ties. So one match in one round with two teams playing. This suits both FA Cup usage and the Davis Cup usage others have mentioned.
I think the other thing about 'tie' in this context is that a tie tends to be a standalone 'event' with its own date and attendance etc. So one match in a Wimbledon tournament doesn't, to me, feel like a tie as it is not separate enough. (At least until we get to quarter-finals etc, and they have their own words already!!) Also it doesn't involve 'teams' as such - although I concede doubles could be considered teams, at a stretch.
I think it is totally different from a 'meet' or 'competition' as I think by definition these have more than two teams involved and a 'tie' has two and only two.
As for whence it comes, sorry, cannot help!
