An irregular demonym is a demonym that is irregular, that is the demonym is different to the nationality adjective. There are a few of these in English, mostly relating to countries and territories in Europe. Some of these have separate masculine and feminine forms which form masculine-feminine pairs ending "-man" and "-woman" respectively, though others are dual gender.
|Britain/the United Kingdom||British||Briton (formal), Brit (informal)|
|Isle of Man||Manx||Manxman||Manxwoman|
|Scotland||Scottish or Scots||Scot|
Generally these just have to be learnt.