If headphones include a mic, does that mean they're for telephone and not music?

Factual Questions
1

If headphones say there is a mic included, and say that they can take calls, should I think of them as hands-free telephone headsets and not for listening to music?

I want headphones just for listening to music, though I might use my cellphone as the source. I don’t want a microphone sticking out in front of me (though in the illustrations of many headphones with mics it’s not clear there necessarily is one).

I’m looking for wireless headphones with noise cancellation. To have noise cancellation there has to be microphones of some kind on the exterior, though they wouldn’t be down where my mouth is. If they say the headphones can be used to take a telephone call, are they doing some trick thing to use the noise cancellation microphones? Or does that necessarily mean there’s some clunky microphone boom in my face?

So, should I rule out headphones that say they can take calls and include a mic, even if I can’t see one in the product photo, because it means they’re telephone headsets and not hi-fi? Or have mics and the ability to talk on the phone become some sort of trick electronic feature that does not impugn headphones for hi-fi?

Thanks!!

2

Headsets with mics tend to be of lower quality than “music-oriented” headsets because they target a different part of the market, but beyond that, you don’t have to purposely avoid a mic if you otherwise like the headset.

3

I had a lovely pair of behind-the-neck headphones that had a mic that you could plug into them for phone use. The downside to phone use was the creepy experience having the other person’s voice seem to be inside my head.

4

Headphones with mikes are useful in gaming as well.