OK, so this is a complicated question because with Britain we have an incredible level of archaeological detail. I'll give a very simplified version and am happy to expand on anything you would like.
OK, so broadly speaking "Celtic" is a language group which incorporates the modern languages of Welsh, Irish, Cornish, Breton, Manx and Gaelic. Befire the Roman expansion however the Celtic languages spread from more-or-less eastern Spain all the way to Austria. Remember this is a language family and not a language, so think "Romance" rather than "French". In Britain, Celtic languages were spoken at least south of Scotland (will clarify soon) and possibly across the entire island. This language family is more or less correlated to the La Tene archaeological culture, so there seems to have been a real cultural complex spread across much of what is now northern and central Europe.
"Gaul" was the Roman word for the territory of more-or-less modern France with some expanded borders, and the Gauls were those who lived within. Immediately before Roman conquest, southern Britain was very tightly bound to Gaul, to the point that southeast England was considered "Belgic". Because of this, it exhibited an unusually high level of material development that made it really distinctive from the rest of the island. To be absurdly simplistic, we can divide Britain into four major zones: southern England, in the "Belgic" zone, the decentralized and less materially rich zone of northern England, the still less materially rich zone going into Scotland, and then the densely populated and materially rich zone of northern Scotland and the islands. So even though much or all of the island was Celtic speaking there was a great deal of diversity in lifeways and culture.
The Picts emerge near the end of Late Antiquity and in the Early Middle Ages. they are a somewhat "mysterious" group in that establishing their cultural geneology and even their language is extremely difficult. They were probably the descendants of the Caledonians of the Roman times, but some have even suggested their language was non-Indo-European. They were certainly considered distinctive by Bede, who divided the peoples of Britain into fives groups of the Latins, Angles, Welsh, Scots and Picts. They are, unfortunately, a bit of a tangle to understand.
