But going back to the OP, there are many new words added to 'yoga' to describe it or to market it, besides the differing schools using different words.
Other schools have raja yoga, kundalini yoga, hatha yoga. and more. Modern ones are like hot yoga, naked yoga, power yoga, moksha yoga, strength yoga, etc. As well, there is probably some overlap and differing understandings. For example kundalini is such a cool sounding word that it might be good for marketing, but in reality very little of it's traditional understanding, if any at all. Yoga is in the top 10 economic growth industries in America today.