Hunter, red squirrels are different from fox squirrels. Reds are about the size of large chipmunks, and MEAN. They chase everything away, and can cause a lot of damage to houses and other structures.
I was going to say this also but you beat me to it. Fox squirrels are the biggest (tastiest) squirrels around. Red squirrels can ruin a cabin in the woods. They gnaw their way into the roof and just cause damage.
Years ago my in-laws had red squirrels all around their home in the boonies. They got in their camper and destroyed it. So I was given the (fun) task of ridding them of the little devils. All they had was an old single shot 12 ga. Stevens (or something) and I brought my trap loads when we visited. I shot 3 a day every day I was there for three summers and finally got rid of them. They are wily little buggers and you have to have a good hiding place but it was fun. Also got rid of their golphers and chipmunks for them.
And we have squirrels playing all around us during deer hunting (oak woods). There is a bunch of black ones now. Basically gray squirrels only all black. Those genes must be dominant over gray because we see more and more of the black ones each year.