Actually, yes they are. The Scottish are descended from the Celtic British population that inhabited the British Isles and Ireland before the Romans invaded. After the Romans left, the Angles invaded who were a tribe of Saxons (hence Anglo Saxon). The Angles then pushed the Britons westwards where they took refuge in the mountains of Scotland and Wales and in what is now Cornwall. Many fled to France and founded Brittany. After they’d taken over most of Britain, they named their lands Angle-Land and they were called the Aenglish. This over the next five hundred years got shortened to England and English.
But they are definitely different races, the DNA of a Scottish, Welsh, Irish and Cornish are distinguishable from the DNA of an English person.
This isn't true and is really old fashioned history from the Victorian period
The people of northern western Europe are north western Europeans, descended mostly from pre Roman tribes and that includes the English. They are all very much the same race, proven by recent DNA studies. "Celt" is not an ethnicity or race anyway and never was. It is a language branch and time period.
There is very little evidence for a large scale replacement by Anglo Saxons in Britain. Before DNA research it was assumed graves in an A-S style must have contained A-S's but we know now this isn't the case, especially with a common grave
Ancient burial practices do not indicate ethnicity, but rather culture. For example if someone in the USA now was to be buried with their Samsung phone, this does not make them South Korean, or someone in Brazil buried with BMW car keys does not make them German.