Can you claim home ownership of a mobile home in a park while paying rent for the pad or are we just considered renters?

You are a home owner. While there is no federal deduction for your space rent, state rules differ. There is a renter’s credit available in California for space rent, for example. 

Yes, you can claim homeownership for your mobile home.  You will deduct any mortgage interest payments as an itemized deduction on Schedule A. If a portion of your rent is for taxes you may deduct the tax along with any tax the state or local government may assess on your mobile home.