There's no competition or reason for competition between the two sites so there's no reason to be worried about mentioning TheHighRoad on TFL. There's certainly no rule against it.
On the other hand, TFL doesn't allow forum wars (arguments about which forum is best, which one is worst, why my forum is better than yours or why the members there are nicer than the members here, etc.) because that's not firearm related.
The two forums are very similar in many respects, significantly different in others. I'm a member of both and enjoy interacting at both sites. Most, if not all of the mods here are also members at THR, and a few are even mods on both forums.
The two sites are related--at least they were loosely related when THR was started. At one point, TFL was shut down for an extended period and THR was started during that interval. A large percentage of the displaced TFL membership joined at THR and a good number of the original THR staff were ex-TFL mods. That accounts for much of the similarity. The differences are the result of gradual changes as the two sites have naturally evolved over the years.
Hope that answers most of the questions.
I'm going to lock this, not because it's a rules violation but because I don't want it to degrade into a "which forum is best" argument.