Hookay then, here goes ( as good as I can get it anyway!)
In the old days of black powder, the first number was usually the caliber IE. 40/65 , and the second would be the charge of black powder , in this case, 65 grains.
When you had three numbers, , such as 45/110/2 7/8, the last number would be the case LENGTH.
NOW, with the advent of new cartridges, things went wonky.
The 30/3- for example , was a 30 grain charge pf SMOKELESS powder.
BUT, your 22/250 has nothing to do with the powder, but that fact that it is a 22 caliber bullet with a 250 savage case that is necked down.
The 25/06 is a cartridge with a 25 caliber bullet necked down from the 30'06 case.
the 17HMR stands for 17 caliber Hornady rimfire, NOT to be confused with other rimmed 17's, or the 17 Remington, which is a center fire cartridge!
the .223 Remington is a case that was actually designed for military use - the 5.56 Nato, and Remington and hung their moniker on it. it uses a .22 caliber bullet, but is center fire primed.
Same as the 7.62 Nato, a 30 caliber cartridge that Winchester grabbed and called the 308 Winchester.
There are dozens more , and most of them can be confusing at times.
the 270WSM and the 270 Winchester take the sane caliber bullet , but one is a short beltless magnum, and the other is a standard sized case from tue 30'06.
Then you have your rimmed, rimless, rebated rims, and belted magnums....
My suggestion would be to buy a book called cartridges of the World.
it is not only a very interesting read, you can use it for referencing all sorts of good info!
Cat