If by record vocals you mean listen to themselves while singing (tracking), they can use absolutely any closed-back headphones for that. In fact, you might use something with stupidly exaggerated bass on purpose to make the singer think they sound better than they do and get them into it... Or patch them into a signal wet with lots of EQ/reverb that isn't actually going into the recording side.
Most artists do not mix their own music. In fact, almost none do unless they're poor/upstarts.
The people who do mix the music (engineers) primarily use external monitors, not headphones.
If they're getting a second opinion from headphones the common choices are HD600, K 702, DT 880 - the same exact "flattish" headphones that are popular here.
For recording/tracking purposes, the only requirement is that they isolate well enough to not experience microphone feedback. DT 770s with their flattering sound and solid build are common tracking headphones, but you can really use anything.
Finally, after the mix has been mixed on monitors, it's a good idea to check it on as many consumer audio devices as possible to make sure it works on the widest array possible, including bassy boomboxes, crappy headphones, offbrand wannabe hi-fi/surround sound systems, badly vibrating car stereos, etc. They aren't mixing for these because they sound good, but because they know people will inevitably listen through them.
Interesting to know Here some pics if anybody cares;