Both Forest and Mansfield are local rivals, but it's hard to have a proper rivalry with a team you never play. Rivalries play out on the pitch, otherwise it's all just talk. When I was a kid, I don't remember there being any rivalry with Mansfield, simply because I don't remember us playing them in meaningful games. They were just the small team we beat in the County Cup semis. But now we're playing them most years, and losing most times, the rivalry has grown. Of course if we ever play Forest again, it'll mean way more than any game with them up the road, but that doesn't look like happening anymore.
And unsurprisingly we hate chesterfield more than anyone else. But hopefully they'll serve their time in the dopths of non league and we won't see them for a while. In the interim I'd happily consider notts as our main rival just to piss off the spires, who think that their main rivals are the blades, when.in actual fact it's more like alfreton.
As far as my rivalry with county goes, its friendly as it is with most stags fans, that's why I do t believe the two morons who attended your game are stags fans.