Does it rotate the same direction as your old one?

Yes. The problem I see now is the wiring. The old motor had no wires coming off of it, instead two "outlets" where you plug the wires in. The new one has a lead with 3 wires coming off of it. When my phone charges I will send photos of the old and new

Motor I just got

Here's what I found on the side of the old one (there were no wires coming out)

You got conned, there is no such thing as rebuilt or refurbished motor for residential. They churn these motors out by machine (brand new) in factories in china and other remote places. Labor makes rebuilding motors a waste of time. (You can't rebuild one cheap enough to compete with a new one.)

What you have won't work. Top one looks to be A/C motor, lower one is D/C motor.

Likely what you bought was a motor pulled from an old piece of equipment in which the motor still works. (hopefully, but without the proper control and voltage requirement of the motor... you'll never know for sure.)