The definition for those depend on who you ask, but in this sub, IEMs usually refer to earphones that create a seal in the ear canal, usually with foam or silicone/rubber ear tips (see airpods pro). Earbuds are earphones that do not create a seal (see airpods).

In live music settings, IEMs are usually used for monitoring. On a stage, it is extremely hard to listen to what you are playing, so IEMs help musicians listen to themselves. They are usually comfortable, slim, and durable. Sound quality is usually NOT a priority: they just need to hear themselves, and that is a low bar. Some sound good, others not so much.

This sub is more oriented towards enthusiast-focused IEMs that offer a good listening experience. Durability and sound isolation also differs, but if you are just using them for listening pleasure only, its fine.

You can't really compare headphones and IEMs as they have different use cases, comfort, portability, etc.

Musicians generally use what's referred to as CIEM, or Custom In-ear Monitors. You get silicone squirted into your ear to get a mold of it and ship it to your company of choice and they'll hand craft you the monitors you've picked. That way they'll (hopefully) fit you perfectly when you're jumping around on stage and offer you great noise isolation to keep your ears safe.

Any one can obviously get these, I have a pair and I'm the farthest from a musician there is.

Sound quality wise they'll run the gamutm depends on how much money you want to spend. You can easily spend over $2k or as little as a few hundred.

Now you obviously don't have to go the custom route. That's just a niche market. IEM's are avalable from a few dollars to thousands upon thousands of dollars. As with everything there will be pros and cons when compared to regular headphones.

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When you're playing live you need to hear two things: 1. yourself, 2. the rest of the band. Traditionally this was handled with stage monitors, wedge shaped speakers on the stage...but this clutters up the stage impairing your mobility and its loud which will eventually damage your hearing...so more often now, musicians use IEMs connected to a wireless rig which gives them better mobility and protects their hearing. Often a band might want to play to a click track which works well with IEMs.

The monitor mix is pretty important, if it's not good you can have people playing too loudly/softly and singers singing out of tune. The mix also might not be what one would think of as good for listening to but it's good for monitoring.

Wearing IEMs does disconnect you a bit from your audience though. I've seen John Mayer playing wearing headphones only covering one of his ears.

Usually earbuds use one speaker for the entire range of sound output which can cause the sounds you listen to, not have deep bass, high treble, or mids depending on what the bud is tuned for. IEM's on the other hand can have several independent speakers. IEM's are not just for instrumentalists who need to hear their parts anymore. It's much more consumer based now and IMO has already made earbuds antiquated. Depending on your budget I could recommend you a pair to purchase and try out.