There is also NRA highpower match rifle. Usually fired with aperture sights (no scopes) where you shoot "Across the Course" or National Match Course (200, 300, and 600). Bolt 308s were popular in the past for this type of competition, but advancements in smaller caliber bullets (specifically .22cal, 6mm, and 6.5mm/.264cal) have given way to other cartridges. Only support allowed is a sling (no mechanical rests).
There are also variations of NRA long range, which is usually fired at 600, 800, and 1000 yards. Fired with aperture sights without rests from prone.
F-Class is still in it's infancy, but is most likely going to become more predominant in the near future for many reasons. For one, you can pretty much use any off the shelf rifle with a bipod and compete. NRA highpower requires very specific sights and other equipment that require a bit more startup capital if you don't already have a rifle designed for it. Second, F-Class isn't as physically demanding as NRA highpower. While NRA highpower doesn't require much physically compared to other sports, it does require the shooter to be able to get into positions from standing (sitting, prone), use a sling for support, and shoot standing without support. Also, NRA highpower requires shooters to move "Across the Course" during the competition, from the 200 to 300 to 600 yard lines after each stage of fire). Whereas F-Class allows the use of rests (such as a bipod) and is only shot in the prone position. This is great for elderly shooters and those who are physically disabled in some manner.