Great Britain consists of England, Wales and Scotland; and the UK is “The United Kingdom of Great Britain and Northern Ireland”. This map shows nicely how it breaks down:
Scotland held an independence referendum three years ago and voted narrowly to remain in the UK (55%-45%). But post-Brexit, the choice for Scotland is to remain either in the UK or in the EU. So when the unavoidable 2nd referendum is held, it seems at least fairly likely that Scots will vote this time to leave the UK — so they can retain their larger trading partner and a more global vision.
The Irish situation I understand less well, but I will take a stab at explaining it, and hope someone will chip in if I make a mistake. Ireland is an island consisting of two countries: Northern Ireland is part of the UK and has close ties to Britain; and the Republic of Ireland (in the South; also known as Eire in its own language) is a separate country with its own government, part of the EU in its own right. (This is why financial companies are looking at relocating from London, England to Dublin, Ireland.)
The reason for Ireland being split is that the North was kept by the UK after the Easter Rising of 1916. While the Republic does not want to be part of the UK, there is ongoing disagreement in Northern Ireland between those who do and do not. But now that being in the UK means being out of Europe, there is less incentive for the North to want to remain in the UK and more reason for it to want reunification with the Republic. As the Irish population has aged, and older people have died, my sense is that a lot of the historical hostility between those in Northern Ireland who do and do not want to be part of the UK (Unionists and Republicans respectively) has decayed, so reunification had become more feasible a year ago than it was a decade or two ago — and then within the last year became much more feasible again than it was when we were all in Europe.
So there is a good chance (I would guess better then 50-50) that Scotland will leave the UK in the next few years — possibly as quickly as they can, so they can remain in Europe rather than having to go through the process of joining from the ground up. And there is a less predictable chance that Northern Ireland will also leave the UK — to go it alone, or join the EU on its own, or reunify with the Republic (which would bring it straight into the EU).
Putting it all together I would not be at all surprised if in a few years, “The United Kingdom” no longer exists at all (due to the loss of Northern Ireland) and “Great Britain” consists only of England and Wales.
(Oh, and that have been rumblings from the Welsh assembly about an independence referendum in Wales, too. So it’s possible that Great England, as it will inevitably rebrand itself, will be left alone — maybe the only country in the British Isles that is not part of the EU.)
Obviously all this is catastrophic for numerous reasons, and you would think the UK government would have considered all of it long and deep before making its move. And you would be wrong; May’s government has not only completely ignored the Scottish and Irish issues, it seems to have gone out of its way to actively antagonise particularly the Scots, denying them debating time in the brief discussion of the Article 50 bill, for example. It’s been so obvious that some people have theorised that Theresa May actively wants to force Scotland out of the UK. I think that is conspiracy-minded, though: following Hanlon’s razor, I think it’s more likely that she is just incompetent: tone-deaf to the implications of her own remarks.
Anyway, this is where it leaves us: with a historic union on the verge of break-up. Not the EU: the UK.
Note 2. Thanks to Niall Hawthorne for corrections on the Irish background.