The anglo- prefix

I have a question regarding the use of the Anglo prefix. in the word anglo-saxon, it describes a mix of Angles and Saxons, right? and so some centuries after the adventus saxonum, the word England in some shape or form emerges, and so the prefix shifts from having anything to do with the ethnic group the angles, and is now denoting that something is English. So for example the anglo-normans are the English Normans so to speak. Is this more or less correct?