It's another name for fairy. They have all sorts of types and behaviors depending on the mythology they're from. Some are tricksters who kidnap children from their homes and eat them or turn them into fairies, others are helpful forest or elemental sprites, some are demons, and some are changelings, taking the form of humans or animals whenever it suits them. As well as some other variations of fae depending on their origin.

One of the more common beliefs is that, if you give your name to a fae creature, they own your name and thus you, giving them complete control over your body. Which is why you never give out your name to a fae. They might march you off into the woods against your will and you'll never be seen again.

Another common belief is that fae can't touch iron, so it's a good ward to keep them away. Hence Columbo never carrying a gun.

They're magical creatures, so the fact that Columbo seems to always be where he's needed or produce what he needs from his pockets seems almost like fairy magic.

Fairies. Generally absurdly powerful magic beings. Commonly assholes or outright sociopaths to those that attract their attention.

Fairy folk - in traditional mythology, fairies and the like aren't sweet little pixies, they're very alien fellows who abide by strict-but-seemingly-arbitrary rules. To differentiate them from modern conceptions, the older term 'fae' is often used for traditional fairies.

The power of words and contracts are common themes with the fae, and often in mythology knowing their 'true name' gives power over them, so they're reluctant to give away that information.