Irish cottage knitting = lever knitting = armpit knitting = production knitting = many other terms.
Basically, it's a style where the right needle is anchored in some way, whether in a knitting sheath, belt, or the knitter's armpit (sorry...) and the right hand is concerned solely with the yarn. The left hand is concerned solely with the left needle. I've taken a class with Stephanie Pearl-McPhee, one of the few proponents of this style, and she flies like the wind!
She gave us the terms which I've listed. According to her reading and research, this style of knitting (right needle anchored) was the predominant style during the centuries when so many people earned wages from hand-knitting, particularly socks.