The Celtic nations consist of:
Isle of Man (Gaelic)
In the beginning, the Celts were divided into different subsects who lived on the European mainland. One group made their way to Ireland whilst another group settled in what is now England..
The group which arrived in Ireland was called Goidelic or Gaelic. Those who settled in what was then Brittain were called Brythonic. The Gaels then migrated from Ireland into what is now Scotland and The Isle of Mann. The Brythonic were driven out of all of it except Wales and Cornwall by Gaelic and Anglo-Saxon invasions.
The descendants of the Gaels are found in Ireland, Scotland and the Isle of Man. The descendants of the Brythonic are found in Wales, Cornwall and Brittany. These groups of Celts are the only major Celtic peoples left, as the ones who stayed on the mainland of Europe were conquered by the Romans and later invaders.
"Celt" is the broader term that include Gaels, along with other groups currently found in Wales, France, and Spain and formerly found all over Europe and The Middle East. Celtic people are an ancient people that have a far-reaching influence over many parts of Europe. This includes Ireland, Scotland, Wales, England, mainland Europe, and towards Asia-minor.
Good to remember is that the word "Celt" came from the greek 'keltoi', which translates to "Barbarian", and they as well as the Romans put this name on anybody that was uncivilised or not romanised for that matter, living outside of the Roman Empire.
The Gaels were the last "Celtic" Tribe to settle in Ireland. The tribe that came to Ireland immediately before the Gaels, the Laigann also settled in South west England. The Tribe before the Laigainn were the Erain or Fir Bolg which originated from Belgium. The tribe which claimed the Islands before them were the Cruithin(Ireland) and Picts (Scotland)
There is no evident or proven link between the Celti of Classical sources and the people who now live in Scotland, Ireland, Mann, Wales, Cornwall, Brittany or Spain, popularly identified as Celtic areas today, or indeed their kin elsewhere in the world. These can claim descent from Britons and Cymry or from Gaels and that's about it.