All Xenomorphs in the group are simply red Xenomorphs with no other distinct features. The Red Queen is .75x the true Queen's height and has armour half as potent as the Queen's.
The only motives that the Red Army seem to have are killing the Xenomorph Hive, and anyone who dares stand in their way. While the Red Xenomorphs from the comic series, Aliens: Genocide, had valid motive, the Red Army following along the events of The Ultimate Hunt are more of anarchist-like Xenomorphs, and do not hesitate to rush straight into a bad situation for other opposers of Xenomorphs to make their lives even more miserable.
Being mutated versions of their Xenomorph counterparts, the Red Xenomorphs have picked up a few abilities that their unfortunate former brethren lack. Any member of the Red Army possesses the ability to spit lethal amounts of acid, which contradicts the class-based restrictions of the Hive for the sake of outwitting and outgunning their opponents. The Red Xenomorphs can also mimick human speech to an extent, albeit poorly. This seems to be enough to lure in unfortunate victims and Xenomorphs, however.
The Red Army rose to relevance years into the events of The Ultimate Hunt, and have been a problem to the Xenomorph Hive ever since. Their first act of defiance was an attempt at striking the heart of the Xenomorph Hive, which backfired immensely and forced them to retreat into the Sahara Desert. They are currently planning another attack on the Xenomorph Hive, of which they hope will cripple it permanently.
While it's not proven for a fact, "Hannah" and Celtic conspire that the Red Army was genetically engineered, (similar to the K Series From AVP: Extinction) as a means of disposing of the Xenomorph Hive. The mystery surrounding the Red Army has yet to be given background, and many choose to believe that they're a failed attempt at a final solution.