This was a discussion that an American College brought up (Brian S Redd) brought up a particularly popular DJ Youtuber who stipulated perhaps we should drop the term 'disco'. The argument is disco is an archaic term now and conveys an idea of what you might get.
Above I've taken 2 pictures (They're both of me I'm afraid to say but hey I had to start somewhere, I'm also happy to report I've moved on leaps and bounds since then I did not stay that way for long, but that was a long time ago). It's argued that maybe the picture on the right represents what we think of when we say disco. To be honest that's what I think of or worse.
Is there a difference?
Well that depends on what you perceive to be a difference on the whole I think in the UK there terms mobile DJ & mobile disco are quite synonymous with each other with little if any nuanced difference between the two terms.
What I've learned is no matter how much we use a term people will use the term they are comfortable with, think about the great bread debate, is Cob, Bap, Roll ect.?
However perhaps it's a thought about what other people think of when a term is used?