There are many differences e.g. if you GA from a visual circuit then you turn downwind, whereas if you GA from an instrument approach, or from a "visual approach" (which is a procedure flown under IFR and without cancelling IFR, but in VMC) then you fly the missed approach procedure which can involve re-entering IMC (which is why a visual approach does not involve cancelling IFR otherwise you would have to get a fresh IFR clearance after GA, before you would be able to climb back into IMC).
Etc...
I have no idea what the definitions are. Definitions of what?
Personally, if I was going missed I would say "Nxxxxx missed approach" to make it clear that I am flying the missed approach procedure, not doing a visual circuit join.