The frock coat [coat as opposed to the frock, which was/ is an undress loose fitting shorter jacket] is in fact [and I believe always was] an UNDRESS garment: not worn on formal parades, but in barracks and as a distinguishing garment for executive officers in the course of their duties. As an example, the adjutant inspecting a Guard mounting before dismissal to Duties. Thus neither Full Dress nor Service Dress.
I am not an expert on officers' finery, but the 1900 Dress Regulations specify a blue frock coat, embellished regimentally but essentially as seen at the wedding, for heavy cavalry, General Officers and staff appointments, most Corps and departments [but not RA, and only regimental staff for RE], and not infantry except Foot Guards. With the abandonment of full dress almost across the board in 1914 and never reinstated I am guessing that such very expensive items either became optional or were not required except by the Household Division and other grandees.
I have in my collection officer groups posed 1900 - 1914 when all present were in the frock coat ........ even in India, dare I add. There has always been a permission/ requirement to wear dress and clothing until unfit for purpose, or while stocks last.
The media do not seem to have picked up that the Princes were indeed in undress ............ as near an informal family occasion as Royalty gets if exposed to public gaze.
By contrast the Duke of Cambridge's thrash was a full state bunfight, hence Home Service Dress/ Full Dress.