Residence Inn: Offers full breakfasts, often times they offer an evening social 3-4 nights per week which will include free wine and beer(the cheap kind) as well as some dinner/snack items. (Think salads and taco bars for food). Their standard room is a studio suite, which has a combo living room/bedroom area, and a full kitchen. The kitchens typically have dishwashers, two burner stoves and a full size refrigerator, microwave and dishes, and a small table and dining chairs. They also have options of one and two bedroom suites. These hotels are set up more for long term stays. I had stayed in one for roughly 500 nights during an extended work project. They're set up like little apartments, and they're the "higher end" version of the long term lodging Marriott offers. Older Residence Inns can feel a bit grubby and don't tend to seem any nicer than most TownPlace Suites. Full housekeeping service will handle everything daily, including loading the dishwasher, and cleaning the kitchen.

SpringHill Suites: Separate living area and bedroom area (often separated by a desk or a half wall), typical continental style breakfast with a couple of hot items (usually that crappy turkey sausage and powdered eggs), no evening social. The rooms are typically more spacious than Residence Inns, and occasionally have a small kitchenette area with a small microwave, a mini fridge, and a little counter space. Some have sinks in this area and some don't. Some have no counter space at all, and just have a microwave and mini fridge in an alcove with the counter space holding the coffee and tea. All suites are typically the same, so most SHS don't have one or two bedroom suites. The newer SHS are really lovely rooms, and the West Elm trundle bed couches they have are comfy and modern. They're meant to be spacious but not especially long-term, in my opinion.

Towneplace Suites: set up more like the Residence Inn, with kitchens, dishes, dining area, studio suites (sofa and bed). They're lower end than Residence Inn, don't offer the same full breakfast spread that RI does, and the breakfast areas typically feel the brunt of the budget-friendly approach. No evening socials, of course. The newer TPS have modern furniture in gray and red hues, and can feel like a nice bargain for the price, especially compared to the older RI. Don't expect full housekeeping service like a Residence Inn. It's usually a light cleaning. ETA: most properties have one and two bedroom options as well.

Fairfield Inn & Suites - they offer standard hotel rooms. (Think desk, chair, bed, microwave, with the TV on the dresser.) You can also get a suite, which would be set up similar to the standard room of a Spring Hill Suite, (separate living area, usually separated by a wall, or a half wall not a door). Standard mini fridge in basic rooms. You may get a microwave or may not. Standard breakfast layout. Maybe a couple of hot items (powdered eggs and turkey sausage etc). Newer Fairfields can be quite nice. They're typically cheaper than Springhill Suites which are often more spacious and the suite is the standard room.

As with all hotels, the unrenovated properties can feel dated and worn down, so it's worth it to compare the age of the hotel as well as the amenities. Service and amenities of a Residence Inn typically offer more than the other three mentioned. Price points would be as follows:
Lower End: Fairfield Inn (& Suites, depending) - standard hotel, Towneplace Suites - extended stay
Higher End: Springhill Suites - standard hotel, Residence Inn - extended stay