There is no general rule.
For example one of the most used DJ headphones (Sennheiser HD-25) never were marketed as DJ headphones. Actually Sennheiser has a line of DJ headphones and the HD-25s are not in it.
When companies make DJ headphones usually they have a few key features:
– Coiled cables (os it does not get in the way)
– Good sound isolation
– most have some way of moving one can of one ear
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However I have seen good DJs use sports headphones, production headphones, in-ear monitoring headphones,…
On the other hand I see a lot of non-DJs run around with DJ headphones.
So the rule is: Whatever floats your boat and supports your workflow and mixing.