MINI Cooper models are categorized using the letter R or F and then 2 digits. This is the chassis code format that BMW uses. There are some inconsistencies but for the most part they are pretty intuitive. Generation 1 and 2 MINIs start with the letter "R" while the generation 3 MINIs start with the letter "F."
Hatchbacks/Hardtops (R50, R53, R56 and F56 models) are defined as any 2 door MINI Cooper that seat 4 and have a 'hatchback' type trunk that hinges from the top of the roof and has a boxy overall shape (not to be confused with the R58 Coupe). MINI started referring to this model as the 'Hardtop' when they heavily diversified in 2011.
Four Door Hatchback (F55) was released in 2015 and is basically a stretched Hatchback with 2 extra rear passenger doors and is sometimes called the 4-door hardtop (totally confusing too). It is NOT the Clubman which has dual barn doors in the rear.
Convertibles (R52, R57 and F57 models) are the 2-door MINI that seats 4 and have a convertible soft top.
Clubman (R55 and F54 models) are the slightly longer than the hardtop MINI model and have either the 3rd door on one side (or 4 door type released in 2016). Clubman have the dual side hinged rear doors.
Coupe (R58 model) seating for 2 and have a large glass-filled rear hatch. This is a less common MINI body style but has a distinctive roof line which some describe as a helmet.
Roadsters (R59 model) are similar to the Coupe in that they only seat 2 but are a convertible.
Countryman (R60 and F60) the larger models that have 4 doors and more bulky appearance. They look like a small SUV and have a taller/fuller body than other MINIs. The Countryman is different from the Four Door and Clubman models and is often confused with the Clubman. Please review the images carefully to confirm your model.
Paceman (R61) is nearly identical to the Countryman but only have 2 doors yet seat 4. Paceman are fairly rare and had a short life span of just 5 years from 2011 to 2015.
Cooper vs Cooper S:
Within each of these body styles are the base MINI Cooper, Cooper S and JCW (John Cooper Works) model. Generation 1 'S' models had a supercharged engine while the Generation 2 Cooper S models had a Turbo. Generation 3 are also Turbo charged. It's best to either look at your MINI and study the following.
Exhaust Tips: One of the biggest visual differences are the exhaust tips on the S model. Cooper S models have DUAL centre exit tips (aside from the Clubman, Paceman and Countryman which have single tips on either side of the bumper). All Cooper base models have a SINGLE exhaust tip.
Bonnet Scoop: In general, the Cooper S models have a hood scoop (functional on the gen1 S and onward just for styling/continuity for the "S" model). However, the Countryman and Paceman MINIs did not have hood scoops at all.
Grill: Grill on the Cooper are typically horizontal slats vs the black mesh on the Cooper S model. Many Cooper owners (gen2) upgraded to the black mesh style grill to make it look like a S. Gen1 Cooper and S model MINIs both came from the factory with horizontal slat grills but the Cooper S model generally (unless it had the Aero body kit) had body coloured (unless it had the Chrome line exterior package) slats while the Cooper had chrome slats.
Side Indicators: MINI will often use more basic looking black or silver side marker housings with orange side lights on the base models and Chrome on the S models along with white or clear side marker lights.
Misc: Base models often have smaller wheels, and will often will have the basic flatter seats vs the sport seats. Also, on models that would allow the S model will have a chrome 'sport' looking gas lid cover and of course the S models should say "Cooper S" on the back vs just "Cooper". Models with the JCW or John Cooper Works kit should have exterior badges on the front and rear and in some cases in the engine bay or interior door sills, etc.
JCW - John Cooper Works: This optional package is available in a range of versions from styling to brakes, body kit, performance and a mish mash of combinations throughout production years. Initially only targeted as a option for "S" models there were some years where certain JCW options were offered to base models. In general S models could be optioned UP to a JCW and there's no definitive answer to what constitutes a JCW for any given model, but in general should have the JCW performance upgrades to be a true JCW, although the wide range of accessories led to some interesting hybrid versions of what a John Cooper Works car really is.
Gen 1 vs Gen 2 vs Gen3:
We cluster MINI models into 3 basic generations describing the major design changes and major model upgrades. Each cluster is listed below referenced by Generation 1, Generation 2 and Generation 3. With few exceptions NOTHING from a Gen 1 MINI will work on a Gen 2 MINI so forth.