These are referenced to Engine makers and specific series that run that engine.
4 strokes could be Honda, Briggs, Tillotson, Subaru or Clone (a Chinese version of a Honda or other make).
2 strokes could be one of a dozen brands, Honda, Iame, Vortex/RoK, Rotax, etc, etc, etc. The list goes on and on.
There are different categories within most 2 strokes. Kid Karts = 50cc, Cadet = 60cc, Juniors = 80cc to 125cc, Seniors = 100cc to 175cc. Most are single gear with a centripetal clutch, but OK = fixed gear on the crank shaft. Then you have Shifters. They start at 80 cc and go up from there. Most shifters are a lever actuated 6 speed sequential gearbox (like a motorcycle), with the exception of Rotax’s DD2 (Two Speed paddle shifter). On a side note, there are 4 stroke gearbox engines also, but not as common.
Within all of these categories and sizes of engines, there may be specific Race Series that run one or another. RoK Cup runs the Vortex engine packages. SKUSA runs primarily the IAME engine packages, but I believe the still allow the Stock Honda 125cc Shifter. In the 4 stroke categories, each Manufacturer has its own series (often piggy backed on with another series) with its own rule sets. TaG is a term used for Touch and Go, meaning it has an onboard starter. This is found on many of the modern 2 strokes these days. It could be on anything from 60cc single gear/clutch to a 175cc Shifter, however when someone references a TaG engine they are typically referring to a 125cc single geared/clutch engine. TaG is usually a mixed manufacturer class where engine parody / performance is accounted for with minimum weight variations.
Its a lot to wrap your head around. Let us know if you have any specific questions