Mess kit/dress is the military equivalent to "black tie" (or even "white tie", which is pretty uncommon). It is the most ostentatious and formal order of dress, normally worn for evening events. Usually, only officers attend these sorts of events, and so it is uncommon to find NCM‘s wearing it. But it does occur, I‘m sure.
A regiment‘s ‘scarlets‘ or Full Dress is the equivalent of "Morning Dress" or "Formal Day Dress", and is normally worn for day-time events such as a formal church parade, Remembrance Day ceremony, etc. This is the next most-formal style of dress, and I am sure that some regiments don‘t have them because of budgetary reasons.
DEU‘s are like wearing a business suit, and are suitable for the majority of occasions and events.
And we all know and love our everyday working dress... combats.
I know, I know, there used to be all sorts of variations and orders of dress, but this is the best I can summarize our current orders of dress as they are right now.
And, I didn‘t even bother including navy/air force, as I know nothing about either. I have seen navy reservists dressed up formally only once, and they appeared to have some sort of double-breasted black coat with shiny brass buttons, but have no idea if that‘s as formal as it gets for them.