"The sons of David were chief officials": what does that mean, and why does 2 Samuel say something else?

This chapter ends, "and the sons of David were chief officials serving the king" (18:17) (tap chief officials). In Hebrew the words are harishonim leyad hamelekh: rishonim is the plural of rishon, which Brown-Driver-Briggs gives as "former, first, chief", and leyad is yad, hand, with a preposition. Rishon is the word for first in 11:6, twice: David said, "Whoever strikes the Jebusites first shall be chief and captain", and "Joab the son of Zeruiah went up first" (11:6). 2 Samuel's list ends, "David’s sons were chief ministers" (2 Samuel 8:18), and there the Hebrew word is kohanim, the word the verse before uses for Zadok and Ahimelech, "were priests" (2 Samuel 8:17); 2 Samuel 8's honest question on that verse sets it out. This chapter doesn't name David's sons here or say what they did, and neither book explains the other's words. This answer doesn't guess.