the answer, as always is
Yes…
(no!)
There several standards.
there are hankerchief heel (turnings) with a v point
there are half round, (not quite round)
there are round heel turnings
there are square (aka Dutch) heel turnings.
there are heel short row heel, and after thought heels, there are German heel, and Welsh heels and Cuban heels…
There are Pointy Turkish heels…there are strong heels, and gurnsey heels… there novelty turnings… there are reverse heels, and inverted heels… and some other styles i’ve forgotten!
There are STANDARDS (but not one standard!)
Pick ONE (any one!) try it.
next sock, pick another
at some point, you might find a heel you really like… and stick with it for a while… but there are endless ways to turn a heel…
Still once you learn a few, you’ll quickly see, many have things in common… and the differences are sometimes subtle…
(and some times radical!)