Yes, they alternate laps. Also, the starting positions are staggered, at least on the short races, to make up for the difference in distance 'round the curves, just like on foot track races. (I think they’re always staggered in oval-track speed skating, but not by much for the longest distances.)
In short-track speed skating, of course, there are no lanes, meaning the guy with the sharpest elbows gets an advantage 