In
Mage the Ascension, vulgar magic is what happens when a
mage forces his will on reality to produce an effect that is normally impossible. While stepping into an alleyway and disappearing under cover of shadows might fall under the realm of
coincidental magic, suddenly becoming invisible in the middle of a well-lit street while you're eating a hot dog is very much vulgar magic.
Vulgar magic is often much harder to accomplish than concidental magic, due to the fact that it is akin to trying to force your way into a crowded phone booth full of drunken frat boys, while
coincidental magic is more like using the courtesy phone a block or so down the street. You have to be VERY good to throw fireballs in Times Square; if you screw up, reality is likely to kick your ass three ways from yesterday in the form of
paradox.