I have a volunteer plant that looks like some kind of vining squash. I've never grown vining squash before so I need some help identifying what this is. Are there different varieties of this type of squash?

Can't help you to identify the plant. But I just want to make sure that you are aware of Toxic Squash Syndrome. If it tastes bitter, spit it out and don't even eat a little bit of it.

Can't say for sure, but it looks like regular pumpkin (as in, jack-o-lantern type). Could that be it?

I agree with Frosti. I think it's a pumpkin.