The three districts in Kootenai County are per Idaho statute. The BOCC (Board of County Commissioners) collectively represents all of Kootenai County.
So the answer is, Yes! You vote for all open positions within the county government.
“…the board of commissioners must district their county into three (3) districts, as nearly equal in population as may be, to be known as county commissioners’ districts, numbers one (1), two (2) and three (3) respectively…” Counties and County Law, Board of County Commissioners, ID. Statute § 31-704 et seq.