Correct. Lungs evolved completely separately from gills. Our ancestors repurposed gills into inner ears, the cartilage of the trachea, and the hyoid bone, all structures still around our jaws/throat.

(Technically, our even earlier ancestors repurposed parts of their gills into the first jaws, too.)

Early in embryonic development, however, our gill arches and their major blood vessels still appear…and the recurrent laryngeal nerve grows out to that embryonic gill tissue. Later in development, the “gills” stay basically in place and become those other structures in the ear and throat. So instead of innervating gills, the nerve is now innervating…all the things we repurposed our gills into.