The Celts were like the Slavs or the Germanic people – a bunch of different related groups speaking related languages, but a “genus” rather than a “species” (if you’ll pardon the misnomer) in terms of classifying cultural groups.
Most of the known pre-Roman peoples of the British Isles were Celts. They fell into certain groups, referenced mostly by language, and then into tribes within those groups.
The Picts appear to have been a non-Celtic group that occupied eastern Scotland up until well into medieval times. There is also thought to have been a group that preceded the Celts in England but of which very little is known – two words, one giving rise to “apple” and the other *ondo meaning stone (whence Tolkien, a scholar of philology, named Gondor and Gondolin in his stories).
Of the Celts, the apparent major breakdown was between the Continental Celts – the Gauls whom Caesar fought in France, the Belgae, the pre-Roman Celts of Spain, the La Tene culture, the Galicians who invaded Asia Minor, etc. – and the Insular Celts. For all practical purposes, the Continental Celts are now extinct, linguistically and largely culturally.
The Insular Celts, which inhabited the British Isles, are broken down into the Brythonic Celts and the Goiledic Celts. The Brythonic group occupied England, southern Scotland, Wales, and Cornwall; the Goiledic group, Ireland. But the Anglo-Saxon invasion drove out or overran the Celts of England and, later, the Brythonic Celts of Scotland; some refugees crossed over to the Armorica Peninsula of France and founded Brittany, where they are still present. The Goiledic Dal Riada people of Ulster, called the Scots, crossed over to Galloway in southwest Scotland, and expanded from there across much of Scotland, giving rise to Scots Gaelic.
A good map of Roman Britain will give the names of the major tribes and the areas they occupied.
That, in a nutshell, is what is known of pre-Roman Britain and its peoples.