What are the main differences between a "DJ" and a "Non-DJ" Headphone?
What are their strengths respectively?
Can I use a "DJ" headphone for daily uses: music, youtube...?
Of course you can
Some general characteristics of a DJ headphone
1) Usually Supra-Aural (On-Ear)
2) Tilting and Folding EarCups
3) Boosted low end
4) Classic v700dj design , which all have been copying since it came out
DJ headphones are usually very uncomfortable (high clamping force blocking outside sound so you don't get deaf during parties) and have unlistenable amount of bass (at least for me). I don't recommend them for uses other than professional.
Some mixed opinions there.
DJ headphones may not be of a low enough impedance to be properly powered from portable devices such as a phone or laptop. Check the rating, if they're much over 50 ohms then don't bother unless you have a separate amp.
It strikes me that you are only considering DJ headphones as they seem a bit sexier, but they're not really. Just with a few features to make DJ's lives easier, like coiled cable and rotating earcup etc.