Gymnastics is governed largely by USA Gymnastics, I have no experience with any minor governing bodies so I wont comment on those. USAG consists of four different types of gymnastics Women's and Men's artistic, Rhythmic, tramp and tumbling and acrobatic.
The most popular (and the only one I have any experience coaching) is Women's artistic, consisting of four event's; vault, bars, floor and beam. All four events are equal in value and add up to a perfect score of 40 overall.
Much like cheerleading there are dozens of possible divisions based on age and level.
Differing greatly from cheer are USAG's requirements. It is head and shoulders above competitive cheer at current. All USAG events must require that every individual athlete, coach, and gym be registered through USAG. While the USASF is in place, this stipulation does not exist at most events. With USAG's requirements of conformity has allowed complete uniformity in judging, that said if a bar routine has a start value of 10.0 and a missed handstand during the routine is a .3 point deduction at one meet it will have the same start value and same deductions at every meet. While true that across the board scoring is universal in USAG judging is not. Judges will vary and score higher or lower than other judges. Where this varies coaches have an option of clarification of judging by challenging the judges score. If the coach feels that the judge was too harsh (I've never seen a coach want their score to be lower) they can challenge and ask what deductions were given, I have personally seen about a 50% rate of increased scores when coaches challenge (the actual number may be higher or lower).
I mentioned start values. Start values come into play in the optional levels. Optional levels are levels 7,8,9 and 10. While compulsory levels are 3-6. Compulsory routines are the same for every athlete in any given level (IE. all level 4's do the same floor routine), while optional routines for all events are, as the name implies, optional. Without getting too deep there are different levels of skills and each routine contains a number of various level skills that ideally add up to 10. If a gymnast has fails to have a start value of more than 9.5 the very best that gymnast could ever do, if they were 100% perfect would be a 9.5. And if a gymnast only has a SV of 9.5 I wouldn't expect above a score in the mid 8's.
Now here's the part you may not care about but I personally feel that competitive cheer should move in this direction. One of start values and consistent deductions and total scoring transparency. Cheer will never lose it's ability to show personality and style but having different scoring levels of stunts jumps and tumbling (inside the current leveling structure) would allow start values to be maxed (I know some companies have started to go to this type of system) and I feel that the quality of cheer routines would explode across the all star world. I'm not sure that I've done a good job explaining this paragraph as I'm a little distracted, I'm sitting in the gym almost ready to spot bars!
If you have any questions I can try to answer them, I've only been coaching gymnastics for about three years so I'm no expert, I have been involved with cheerleading for almost 10 years now so I have a fairly decent grasp on the differences.