Help Identify Barrell Cactus

[Littlefalcon]

I was given this Barrel Cactus and I'm having a hard time identifying the type. I understand there are several kinds, but I am a little perplexed by the pup going off the side rather than from the bottom.I also noted the odd shape of the cactus itself. It doesn't appear to be as round but a bit more oval or oblong. The fuzzy stuff is cat hair LOL not natural hair. Thank you.