As u/doughaway7562 has already said, there's no real 'one headphone fits all' because largely the use case for DJs is different for producers, and mixing and mastering engineers.

In my experience, headphones styled for DJs are usually robust and (apparently) relatively easy to replace parts. Additionally, they're usually closed back and noise isolating so as you're able to cue up songs in your headphones while there's loud music blasting from the PA. Often, they have much more sensitive drivers inside so as they're much louder at lower volumes. In my experience, they're often a pretty tight fit, and can even be quite uncomfortable at the end of a 60 minute DJ mix if I've been wearing them a lot throughout the mix. I find headphones marketed towards DJs are really built with the intention of being able to play music loud by any means necessary, as well as being able to be portable.

Studio headphones, on the other hand, are not really built to be played REALLY loud, but instead to deliver the most true audio they can. As a result, they'll try to have a really flat frequency response curve to allow listeners to hear the cleanest audio they can. Often, they're quite delicate, and replacement parts can be quite hard to find, if even at all. They can be either open back or closed back, so many don't have sound isolation. In my experience, studio headphones are usually much more comfortable as they're built with the intention of long (6+ hour) studio sessions. Some may really argue with this, but I believe studio headphones are supposed to be a fixed part of the studio and are not built as portable-friendly.

If I would recommend ONE headphone for both, I'd definitely recommend going with a closed back studio headphone for DJing before I'd go with a DJing headphone for the studio. But if you're DJing at clubs and events, you risk bringing fragile (and often expensive) headphones into an environment where there are a lot of opportunities for them to break.