Hello!

I was wondering if someone could give me an advice about installing shower drain. This is my first time doing it. I'm basically replacing shower pan/tub and drain assembly. My drain pipe is 2" metal (copper?) and I bought a no caulk brass drain (made by Oatey) form Lowes. I was surprised to find out that it's a lot bigger (by about 1/2") than my pipe. Rubber gasket simply slides over the pipe, not even touching the walls I've read instructions and watched videos on how to do it, and it suppose to be pretty snug on the pipe. Am I doing something wrong, or drain is simply wrong size (it does say for 2" pipes on the label)? Or is it meant for PVC pipes that have thicker walls?
I appreciate any suggestions