In my experience, many (though not all) Springhill Suites have a small bar/restaurant attached or in the building for dinner/evening service, while RIs, TPS, and FI generally don't.

RIs and TPS tend to have full apartment set ups for long term stays (sleeping area, living area, and kitchen with stove), though I've done a share of short stays at both. Though location dependent, as others have said, RIs tend to be a step up from TPS.

To me, Fairfield provides a much more basic service offering room-wise - a basic bed, bathroom, (maybe a mini fridge), and a hot breakfast. (In my experience, room decor is very plain). Basically what I'd expect from a Holiday Inn Express.

Springhill Suites provide at least studio suites, sometimes with multiple rooms. They have a kitchenette or wet bar with minifridge, microwave, and sink, though usually not a stove from what I've seen. (Good for longer term stays I suppose, as long as you're not counting on cooking). For me, I place Springhill suites on par with a Courtyard, though all else being equal, I'd prefer a SHS given the room size and breakfast benefit (and often the presence of a bar/restaurant).