Suites names in hotel brands are for hotels whose rooms are either all suites or mostly suites. It's not just Quality Suites, but also Mainstay Suites also in Choice, plus Candlewood Suites in the IHG program, etc, etc.

Now, that doesn't mean they're all fancy suites, just that they have suite properties such as full kitchens in their rooms.

As I mentioned before in this thread:

Mainstay Suites Is A Conversion Brand?

In Costa Mesa CA there was a Quality (I don't remember what suffix) that became a Country Inn & Suites (in the Radisson program), and then came back to Choice as Mainstay Suites. The difference between Quality Suites and Mainstay Suites is in benefits like breakfast, but both are suites hotels. I think the conversion to Mainstay Suites instead of back to Quality Suites may have been because of breakfast staffing issues, which causes them to suspend the breakfast temporarily, and even when they restored it was much less variety than a Quality Suites/Inn/Inn & Suites breakfast buffet.