For the first 15 years or so of our existance, we were Pet's Mart. Now that we have lots and lots of trainings and manuals to do just to work in the store, we are now Pet Smart
It's neither. According to the company business overview and investor's site pages, it's PetSmart in one word. The 'S' is capitolized so, you might infer a word separation of Pet and Smart.
And, like missyme06 pointed out, it can go any way you want it to. PetSmart's ad agency doesn't need to define the name. They just need to get people to think about it.