Is my hamster part mouse?

He is white with a cream mask around his face. He looks like a hamster, but a little like a mouse or a gerbil. I didn't think anything of it when I bought him. My other hamster, which I bought at a different pet store but at the same time, has slept all day. I was going to try and have one litter of babies out of them, but they completely ignore each other! I don't know what to do! My hamster, who looks like a mouse, is always on his wheel. He has been on his wheel almost nonstop for over 4 hours, in the daytime! I bought him from Petco in Quincy, IL, if that helps. He is much smaller than my other hamster, but I just thought he was just younger than her, but now I'm not so sure. Please help, I need an answer! He has no tail, when I pick him up he squirms much worse than a hamster, more like a mouse, and moves so much like a mouse. I am wondering if he was born without a tail or lost it, and they said he was a hamster. Please help me! Thank you for all your answers!