1. Ulster-Scots, i.e. the Scottish people who moved into northern part of Ireland (now all of Northern Ireland plus a couple of counties in Ireland)
2. Some Irish and some Scottish, i.e. they have ancestors from both places and want a word to describe this
3. Generally celtic, i.e. they know it's Ireland or Scotland or maybe both and want to cover their bases
Neither is particularly harmful, but I kind of wish some people understood that #1 is a distinct thing
if society ever gets this right about northern ireland it will be a good day for everyone :)
(People in those parts of the country are disproportionately likely to be Scotch-Irish, and therefore to have an ancestor who named a child after William III).
This is covered in significant detail in "Albion's Seed", among others.