As said, it is called the .22-250 because it is the .250 Savage necked down to .224. When it was a wildcat, that is how you had to make brass. Nowadays, the .250 is so uncommon that people load for them with .22-250 brass necked up instead.
Theoretically, you could make them out of any standard head diameter case. It would take about $400 worth of dies and a lot of labor to do the job, however.