Amhara and agew similarities and/or differences

Alright so we know that Amhara and agew are close and everything but to what extent. I heard before Amhara and Tigray became a thing, most were agew but throughout history Amhara and agew have lived together side by side. My question is how related are we. For example agew ruled lalibela but was populated with many Amhara people until the downfall of the zagwe and rise of yekuno amlak.

So are Amhara and agew the same people with slightly different cultures? Are agew the predecessor of Amhara and Tigray and the og habeshas? And is it right for Amhara to claim zagwe as their own history? Can someone please explain for me