Great Britain became a common term for England Scotland and Wales when the Scottish and English crowns were united (by James VI 1606?) , becoming the Kingdom of Great Britain in 1707 when the parliaments became united. It wasn't until 1801 with a further act of union that it became the United Kingdom of Great Britain & Ireland, which lasted until 1922 when the Republic of Ireland separated apart from Ulster, forming (in 1927) the present United Kingdom of Great Britain and Northern Ireland. It would be technically inaccurate to describe the Irish (north or south) as being from Great Britain, but for historical reasons Protestants from Northern Ireland will commonly describe themselves as being British.
Where the Manx and Channel Islander's fit in, is beyond me.
British Isles however encompases the whole archipeligo. Confusing?