Western is the traditional system used in Europe and North America. Vedic is Indian, Chinese is, of course, Chinese. There are also some off-shoots and modernized archaic (or purely invented) types that have come into vogue - Celtic and Mayan to name two.
The thirteen signs were introduced back when I was in college, so it's hardly new. And periodically there's a push to bring the 'signs' into alignment with their 'constellations', but since the 'signs' are actually geometric/mathematical constructs that don't correspond with the constellations and haven't for generations, it doesn't much matter what the so-called experts say.
All signs in the Western zodiac are determined from the vernal equinox - when the Sun crosses the equator heading north.
For me, the push to redraw the zodiac is on the lines of not liking varying lengths of months so pushing for 30 day months with a couple odd extra days thrown in - oh, wait, that's what the 31 day months are all about.
