Most of my rings have square shanks. The square shape fits a wider variety of fingers and goes on easier if fingers have some swelling at the joints, because the square shape allows a little more room than a round shape on a finger. I notice that people use square rings on middle or pointer fingers in addition to the traditional “ring” finger. But traditional sizing is more of a challenge, since traditional ring sizes refer to round rings. I am working on a translation from traditional ring sizes to square sizes, but in the meantime, I refer to rings (for women) as extra small (for the pinky on most people), small =ring size below 6, medium= ring sizes 6-7, large= ring sizes 8- ish.
Some of my rings have a slit designed into them that makes the ring slightly adjustable by moving the ring forward and backward while opening a little.