The .38 rimfire / 9.5x22mmRF refers to a family of cartridges that have been in service in the United States since the mid-19th century. The cartridges are produced in short, long, and extra long variants.
Much like the smaller .32 rimfire, the rounds were originally manufactured loaded with black powder. In the early 1900s, manufacturers switched to the "new" smokeless powder.
The .38 rimfire was preferred to the .32 rimfire for hunting and self-defense purposes because of its larger diameter bullet and increased muzzle energy.
^Barnes, Frank C. (2012). Richard A. Mann (ed.). Cartridges of the World (13th ed.). p. 0. ISBN978-1-4402-3059-2.