So, others have mentioned the three most common styles on the English-speaking internet: Continental, also called German (picking; working yarn in left hand) and English/American (throwing; working yarn in right), and combination knitting.
As a commenter said, there is Portuguese knitting. If you have ever seen somebody knitting while tensioning their working yarn around their neck or from a special pin attached to their clothing, or both if using multiple yarns, this was probably Portuguese knitting. This may be the same as Andean knitting. At least, from the descriptions I read, I think they're the same.
There is Russian (https://www.craftsy.com/knitting/article/russian-knitting-technique/?_ct=rbew&_ctp=16072) and Norwegian
(https://www.craftsy.com/blog/2013/05/norwegian-knitting-technique/), which seem similar to each other but not quite the same.
And then there's Lever knitting (also called Irish/Cottage knitting, though some say that's a bit different). I am fascinated by Lever knitting and want to learn to save my arm. I understand it is far more ergonomic. If you've seen someone knitting with one needle under the arm (and probably knitting very fast), this is probably what they're doing. There's supposed to be a way to do this holding circulars, too. I understand this is one of the fastest ways and thus used by a lot of people who knit for a living. For one thing, the knit and purl are supposedly equally easy and therefore tension tends to be better overall. I recommend looking for videos on Lever knitting, as they're as entertaining as they are impressive, but here's a nicely set up webpage with still photos and nice directions: http://www.heartstringsfiberarts.com/leverstyle.shtm
I suspect there are a dozen more ways as well. :-)