I cannot comment on the Annals, but in the Song of Roland, it's clear from the text that the author has very little real knowledge of those the author calls Muslims. He makes all sorts of descriptive mistakes that a person with even passing familiarity would not make (For example, Muslims are extremely monotheistic, yet the author does not seem to recognize this.)

In fact, the poem's main story is about a battle (IRL - The Battle of Roncesvalles) between Charlemagne and Spanish Muslims. Among the many poetic embellishments the author makes is to turn the Christian Basque peoples Charlemagne actually fought into Muslims.

I suspect the answer to your question would be "no" there is no precise distinction made by the author(s) of the Annals, and even if there were, it's unlikely we'd be able to determine what it is, given the confusing nature of their knowledge (e.g. what if the distinction is based on a perceived difference that we do not recognize or understand?).

The word Saracen is so old that its ultimate etymology is unknown; however it is believed to derive from Abraham's wife Sara. The Saracens originally inhabited the Syro-Arabian desert and harassed the Roman Empire. Starting out as a geographical identifier, the term again evolved to mean any Muslim, especially during the Crusades and Middle Ages. This term, more than any, has withstood the test of time due to the fact that the word was coined within the Roman Empire.

Moor is a geographical identifier at first relating to persons from Morocco and Algeria, areas in Northern Africa, and is later used to identify Muslims from that part of the continent.

Just some background info...not sure about specific Frank usage.