But Wesley would never refer to that as his first command, would he? Command, in that sense, has always meant their first ship.
Nope - according to McCoy and Spock both, Spock's first command was in "The Galileo Seven"... However absurd that may sound in terms of Spock's career.
That's perfectly normal real world usage, too. Most commands in the military, or even in the Navy, are not going to involve ships of any sort.