There may well be a difference between the Reachmen in different parts of the Reach, as they're not solely of Breton descent; some may have Orcish ancestry, and others may have Nordic ancestry (though comparatively weak due to the fall of the First Empire of the Nords; Nord colonists were wiped out from the area), but they are all "of Breton stock".
I should probably add (while not totally relevant to your question) that the "Western Reach" is not only separated from the Reach by the political boundaries of High Rock & Skyrim, but the literal physical boundary of the Druadach Mountains (which also separates the entire region from Hammerfell).
As for the names of other Reachmen groups? There was the 2nd Era Reachmen dynasty known as the "Longhouse Emperors", though that was very short-lived (2E541~577; 36 years). The only other named Reachmen group I can think of is the "Winterborn", which tried to usurp control of Wrothgar (the Wrothgarian Mountains) from the Orcs.
I would guess that relations between Reachmen and Orcs could be determined as "fairly neutral" throughout history. At one point, they must've been on friendly terms, because the Reachmen did conduct trade with Orcs in the past, and apparently learned "hedge-magic" from them as well. At least one time, as mentioned in the previous paragraph, they also fought the Orcs for territorial control (but that's likely an isolated incident because that was just a single clan of Reachmen rather than a united people).
Has there ever been a time when Reachmen and Orcs united against a common foe, however? I would say "No".