Lots of things in knitting have more than one name, or different things called by the same name - wait till you find increases...
Other names for Long Tail CO are slingshot, from how it looks in your hands - and double CO because you use 2 strands. I think there's a couple more, but I can't remember them. The knit and cable COs can put the new sts on with the tips pointing toward each other, or with the tips parallel. The Lace CO is the knit CO with the tips are pointing at each other when you put the new stitch on.
Vicki's single CO is shown on this site by Amy as the 'thumb alternative' or english Long tail CO. I do it like that, maybe it's called 'single' because you only use one needle. And yeah, her 'knit' CO is really a cable CO. People call that a knitted CO because you sort of 'knit' the stitches on the needle, except the other needle tip goes between the sts rather than into the end stitch which is usually what's known as the knit CO.
sue- knitting heretic