People from Britain are referred to as British.
However I recently learned that Britain is not technically the same as Great Britain.
Great Britain and Britain do not mean the same thing. Great Britain is made up of Scotland, England and Wales, where as Britain is just England and Wales.
Source 2 (emphasis mine)
Great Britain is the official collective name of of England, Scotland and Wales and their associated islands. It does not include Northern Ireland and therefore should never be used interchangeably with ‘UK’ – something you see all too often. Here at Ordnance Survey, we’re responsible for mapping Great Britain, which is why we don’t make maps of Northern Ireland. Technically, if you lose the ‘Great,’ Britain only refers to England and Wales.
So is it accurate to describe someone from Great Britain as Great British?
I've certainly never heard it. But I wonder if there was ever a time when the phrase was ever in common usage? (NGrams seems to suggest it was most commonly used in the 1830s- although some of these uses are for objects not people.)
Update: It seems my question has sparked an side-argument about exactly what the differences are between "Britain" and "Great Britain". This was not the intention of the question. I simply wanted to ask whether it has ever been acceptable to call a person "Great British".