This should be very self explanatory, if i remember correctly the celts had been present over most of western europe, including Ireland and Brittany, im aware that the bretons, Cornish, and Welsh are celtic, but what seperates the irish and scots from the celtic family?
Not to discourage any further answers but you might like these older posts:
Did the Celtic peoples "arrive" in Britain, or did Celtic culture just spread to the bronze-age inhabitants of the island by /u/amusiclistener
What caused the Celtic expansions across Europe, and then the later Germanic expansions? Were there any shared causes? by /u/Miles_Sine_Castrum
A simplistic answer is that the Gaels were Q-Celtic speakers while the Britons were P-Celtic. Q-Celtic is considered to be the older branch of the Celtic languages so it makes sense that it survived amongst the Irish who are the most westerly of the Celtic people. We say Q-Celtic, but for practical purposes we're dealing with C mostly. eg. Briton, Cruitin and Map, Mac.
Scotland is a jumble.
It's likely that it was originally a Britonic region with everyone speaking a P-Celtic language. The problem is that Q-Celtic was spoken in Ireland and there was ancient contact between Ireland and what later became Argyll so we can't be sure that Q-Celtic wasn't also being spoken in ancient Scotland.
The Romans conquered the southern part of Scotland and built two walls.
The people beyond the northernmost wall were referred to as the Picts. They were likely just Britons who retained their culture in a more pure form than the tribes further south, they didn't become Christian for instance.
It was the Irish who went amongst the Picts and converted them to Christianity and likely sowed the seeds for spreading Irish culture because eventually the Picts were Gaelicised and this Irish speaking people made up of the Picts and Irish colonists established the Kingdom of Alba which in Latin was Regnum Scotiae - later Anglicised as Scotland.
The initial Kingdom was similar to the region the Romans never occupied, that is Scotland north of the Forth/Clyde line. There was a later settlement of Irish (mixed with Vikings) in Galloway who also brought their Irish language with them.
In the early part of Scottish history there were still Britons speaking their P-Celtic language from Glasgow south into the Lake District which is now part of England. The area south of Edinburgh though was English speaking as this had been conquered by the Angles and became part of the Kingdom of Northumbria. It was the Viking invasions which allowed the Scots to take the northern part of Northumbria.
P-Celtic is thought to have died out in Scotland around the 13th century which is also when Gaelic was probably at its height and most widely spoken. It was around the 16th century that Scots stopped referring to the Gaelic language and culture and started referring to the English speaking population.