These two get used interchangeably in quotes and catalogues, and they behave completely differently. Ordering the wrong one wastes an entire run.
Glow in the dark
A phosphorescent pigment absorbs light and releases it slowly, so the design glows in a dark room after being charged under any light source.
It is pale but visible in daylight, and the glow fades over time as it discharges, recharging whenever the lights come back on.
UV reactive
A fluorescent pigment that does nothing on its own. In daylight it is nearly invisible; under a blacklight it lights up brilliantly.
In a dark room with no UV source, a UV tattoo does absolutely nothing at all.
How to choose in ten seconds
Does the venue have blacklights? Buy UV. Does it not? Buy glow.
That really is the whole decision, and it is worth checking with the venue rather than assuming, because a marquee with festoon lighting and a club with UV bars need opposite products.
A note on expectations
Neither is as bright as the product photography suggests, because photographs of glowing things are always long exposures.
Both are genuinely effective in the right room. Ask for a sample and look at it in the actual venue lighting if the order is large.