Sir Edward Carson, who led the threat of armed rebellion against the Crown in the period 1912-14 if a very limited form of Irish home rule were to be granted, envisaged the subsequent partition in 1920 as creating an Ulster Orange state in the north of Ireland. But this aim had to be abandoned when the Unionists broke up the ancient nine-county province of Ulster by refusing to accept the counties of Donegal, Monaghan and Cavan, with their massive Catholic majorities, while insisting on incorporating Fermanagh and Tyrone, with their smaller Catholic majorities, into the new statelet because a grouping of only the four Protestant counties would not have been viable.
The Government of Ireland Act, 1920, created a new six-county statelet of Northern Ireland and makes no mention of Ulster. There has never been a Secretary of State for Ulster, only one for Northern Ireland.
So it was historically and legally bogus, a sop to dignify the position of the Unionists, to allow the continued use of the word "Ulster", where they themselves had made it obsolete. The police force that took over from the Royal Irish Constabulary at partition should properly have been named the "Royal Northern Ireland Constabulary".
David Trimble once berated a journalist for referring to him as the "Northern Irish" politician. He insisted that he was British and therefore a "Northern Ireland" politician, yet he blithely embraces the appellation "Ulster", which applied to an Irish province. He is also annoyed because the Irish harp and shamrock are to be removed from the RUC's cap badge.