What’s the difference between Old English and Anglo-Saxon?

There is no difference at all between Old English and Anglo-Saxon. Anglo-Saxons were the people who spoke Old English in parts of what we know today as England and south-western Scotland thus we sometimes refer to Old English as Anglo-Saxon. The term Old English, however, is often informally used to refer to other historical forms of English such as Early Modern English/Renaissance English (Shakespeare), Middle English (Chaucer) and in the strict historical sense this is not the right terminology. The Present-Day English is the term we use to describe Modern English and is the language as spoken today.

Old English is a West Germanic language. Danish and Norwegian settlers in Britain spoke Old Norse language that influenced Old English and reduced in time the number of inflections originally occurring in Anglo-Saxon which similarly to modern German had endings indicating words’ roles in the sentences, their grammatical gender and number. After the Norman Conquest of 1066 the large number of Latin-based words influenced Old English and further resulted in the temporary dominance of French. By 1150 Old English was no longer used.