Some are the same diameter, but more powder. For instance: in a .357, you can shoot either .38 OR .357-the diameter of the round is the same, the charge is just bigger for the .357. However, you cannot shoot a .357 in a .38 chambered pistol, due to the added stress & longer cartridge of the .357. Same with .22 & .223. You can get conversion kits for AR type rifles that replace the bolt & you can effectively fire .22 out of it (with special magazines as well). The neck diameter is the same-the .223 is simply longer, and more powerful.
There are conversion kits for some pistols as well-it is simply a matter of replacing the barrel. I have read elsewhere of people doing a 9mm to .45 conversion on pistols, but have no first hand experience with that.