Yes, they're distinct _within Ireland_, but overall the English spoken in the Republic of Ireland and Northern Ireland is all considered by linguists to be Hiberno-English, and is its own distinct dialect family vs, say, North American English. And Ulster English is even spoken within the Republic of Ireland, which is obviously not part of the UK and is not British at all.

> And Ulster English is even spoken within the Republic of Ireland

Not surprisingly so since Donegal, Cavan and Monaghan were also extensively settled by Scots immigrants, but were cut off from what's now casually called Ulster in 1922. So they had 300+ years of shared language versus 100 of separation.