The Venerable Bede tells us in his history of the English People and Church that different tribes from continental Europe came to England to make their homes and that certain parts of the country were settled by certain tribes, the Angles, Jutes, and Saxons, hence names like West Saxons, East Anglians, and so on, who in turn displaced the native Romano-British/Celtic peoples. This is the view that has come down through history and is widely repeated in less academic writings on the subject. This is the version you see repeated in modern documentaries, textbooks, and popular understanding of this time in history. Only this isn't how it happened, and modern scholarship has harshly critiqued the old views on the subject of the Anglo-Saxon migration.

Robin Fleming talks about how the "Anglo-Saxon migration" was really a broader movement of North Sea adjacent peoples into Roman Britain. This included people from Denmark (Jutland), and Northern Germany (Saxony), but also people from Norway, Ireland, and Sweden. The idea of the Anglo-Saxons as a purely Germanic culture is misguided and not supported by the evidence that we have available through archaeology. She points to the blend of clothing and jewelry styles that emerged following "Anglo-Saxon" migration to Britain as evidence that these two cultures were assimilating into something difference from either that came before. She views this process as more or less a peaceful one. While they was some endemic violence inherent to the time period, she does not see evidence for the mass violence that is often assumed to have accompanied the Germanic migration into Britain.

The idea that the newcomers, be they Angle, Saxon, Pict, or Irish, waded through Roman blood to carve out new kingdoms on the island of Britain that were derived of singular homogenous ethnic groups that were entirely from continental Europe is entirely false.

One thing that is paramount to remember is that these various tribal groups and "peoples" did not form coherent national identities that were set in stone and unchanging. This view of the Angles, Saxons, and Jutes, forming one coherent polity and the British another, oversimplifies the situation to an extreme degree and is an unfortunate holdover of the 19th Century.

So the Saxons of Saxony and the Saxons who settled in Britannia might both speak the same language, worship the same gods, and so on, but they did not necessarily view themselves as the same "people" in an abstract sense of the word.

Peter Heather argues that the identities of these groups were quite malleable in the social upheaval accompanying the end of the Western Roman Empire. Instead of kinship among these disparate groups of people, we should instead see loyalty between the armed retainers of a warlord/chieftain/insert your preferred noun here/ as the most paramount social identity. Status and position as an armed retained, a precursor to the later Huskarls and Housecarls, were much more important that subscribing to an identity of being "Saxon" "Anglish" or "Jutish".