"Great Britain" was the name of a sovereign state
from 1603 (when James VI
acceded to the throne of England
as James I
) to 1707, the date of the Act of Union
between England and Scotland, at which point it became "The United Kingdom
of Great Britain".
In 1801 with another Act of Union the name of the state became "The United Kingdom of Great Britain and Ireland" until 1921 following the foundation of the Irish Free State when it became "The United Kingdom of Great Britain and Northern Ireland", which name remains in use.
The use of the expression "Great Britain" today refers to (or should refer to) the mainland of England, Wales and Scotland plus those of the surrounding islands which do not have some form of self-government: in other words including Shetland, Orkney, the Hebrides, Anglesey/Ynys Môn, the Isle of Wight and the Scilly Isles, but excluding the Isle of Man and the Channel Islands, as well as, of course, the entire island of Ireland and its surrounding islands.