4" OG or Oh Gee as some call it and it comes in several sizes but has a similar shape. I've seen 4", 5" and 6" 1/2 Round Gutter
5 1/4" Fascia Gutter is typically for use on a roof that has 2x4 rafters as when they are cut at a 4:12 pitch the result is a 5 1/4" edge as you can see it come sin two sizes most typically. The photo above is NOT a properly made gutter. The hook edge should be 1/4" lower than the opposite edge before it runs up the roof with the "wing". Properly made the rain water would overflow the exterior edge if the gutter got clogged and not run back up under the roofing materials.
5 1/4 Curve Face gutter is just as it sounds, the curve face became popular for a while and is still sold. It was originally the result of trying to straighten a standard smooth fascia gutter that had a bit if a ripple in it. It would tend to straighten out the wrinkles as it greated the curved face. Then it became popular in it's own right.
5 1/4" Deco gutter has lines about 1" apart creating a "decorative" look.7 1/4" Deco gutter is also available.
Dutch gutter is a very simple angled piece of sheet metal and is typically locatged above entry or exit doors to keep rain water from coming directly onto those entering or leaving the home. This is a very low cost solution and meets the MPS.
All metal roof flashing's, gutters, etc are or should be at least a 26 gauge material. All gutter should be built with the outside edge lower than the inside edge or wing that runs up the roof. This would allow a plugged gutter to overflow the gutter rather than back up onto the roof. If you will notice some of the sketches used in this article don't show that, It is clear the drawings were made by someone who doesn't understand the design process of a proper gutter.