So from what I read, the first people that lived in England were the indigenous celtic Briton, until they were driven off by the Romans which caused them to live in Wales which was apart of England during then. However, the anglo saxons travelled to England in around the late 4th century, but what confuses me is how the anglo saxons were considered English? If they moved to England, how on earth did they get the English ethnicity if they came from different places, weren't the celtic Briton the original, ethnic English people? Why don't the English compare themselves to the celtic Briton but instead they compare themselves to the Anglo saxons? I'm sorry if my question is strange but I tried to find the answer in Google but nothing came up apart from random facts about the celtic.
This is really a question of terminology. "England" doesn't exist as a concept until about the 7th Century, or as an actual place until arguably the early 10th, although there are political rumblings about it in the 9th. The idea of an Anglalond, home of a gens Anglicarum really arises with Bede in the 7th Century who, if he didn't originate the idea, was certainly an early proponent of it. Bede was a Northumbrian who professed an Anglian ethnic identity at a time when Northumbria was the dominant political power in Britain, hence the idea of an Anglalond rather than a Sæxalond or a Jutland. This idea matched Bede (and Gildas') historical narrative: the gens Anglicarum - Bede's Anglian-centric identity for Angles, Saxons and Jutes who shared a common Germanic heritage - carved out a collection of kingdoms from lowland Britannia which thus collectively formed the Anglalond. Our familiar concept of definite and discrete "Angle", "Saxon" ans "Jutish" areas of settlement also come from Bede in this period.
This, of course, doesn't quite match up with the archaeological record. It's worth noting in your question that the Romans didn't "drive the Celtic Britons into Wales". Indeed, most of the Brythonic areas of Britannia were conquered and saw their populations 'Romanise' to various degrees, while the Romans failed to penetrate so extensively into Gaelic areas. The common narrative seen in Gildas and Bede of the incoming English driving the Britons into Wales doesn't really bear fruit either. Evidence suggests that, far from a coherent invasion, the settlement of the English - or rather "future-English" in Britannia was a piecemeal affair that saw newly arrived populations frequently settle alongside and integrate into existing British communities.