Yes,I understand that.I think that many states have a Governor's appointment provision and other states have various other methods.
An interesting sidenote on the subject...in '04,when our (MA) esteemed junior Senator was destined to become President,the (95% RAT)state legislature changed our replacement method...which had for many years been "Governor's appointment"...because the governor was a Republican.
Yet another benefit of living in a one Party state!
One state has a rule that the party of the Senator gets to select three names, and the governor gets to pick which of the three to appoint. Many states just leave it to the Governor.