I hope I have not misunderstood the context. Right now, it appears they are interchangeable, but if there is a subtle distinction I would like to know. Please explain.
They are pretty much identical, but 'demesne' implies a medieval feudal context more than 'domain' does. They are derived from the same word (Old French 'demaine') and pronounced almost identically (doh-mayn vs. di-mayn).
When used by a historian 'demesne' usually refers to lands held by the crown (or a baron, etc) whereas 'domain' has no such distinction.