Holy Cow!
What a huge subject. Cartridge collecting is just as interesting, maybe more so, than collecting firearms.
The variations are almost endless. In addition to Rimfire and Centerfire, there was Pin Fire, Teat Fire, and probably a few more that I can't think of right now.
In Center Fire there were the old Copper Cased, Benet Primed, Folded Rim cartridges, Balloon Heads, and modern Solid Head cases. This photo of 45 Colt cartridges includes one of the Benet Primed rounds at the far left, some Balloon Heads, and second from the right is one of the rounds with the extra large rims made for the Colt Model 1909.
Here is the difference between a Remington-UMC Balloon Head 45 Colt on the left and a modern Solid Head case on the right.
Frankford Arsenal produced ammunition for the US Military from 1816 until 1977. Frankford Arsenal was key to many advancements in ammunition technology in the mid 1800s.
At one time, Smith and Wesson and Winchester made their own ammunition. Winchester still does.
The United States Cartridge Company started operations in Lowell Mass in 1869 and produced much of the ammunition used in World War One. After the war it was acquired by Winchester. I bought this reproduction of an 1881 USCCo poster last year. They had a magazine explosion early in the 20th Century that flattened an entire neighborhood.
Union Metallic merged with Remington in 1912. On the left is a REM-UMC headstamp and on the right is a 38-40 made by the United States Cartridge Company. Notice how the primer is stamped with a US. Pretty neat, huh?
If you really want to learn about old cartridges and the companies that made them, go to this guy's web site. It is terrific. Be sure to check out his picture pages.
http://www.oldammo.com/january04.htm