I don't speak German but was fascinated to learn that in (Swiss or I believe Bavarian) German Rahm means cream, but Rahmen means frame - despite adding "-en" being the normal way to make a singular word plural. Rahm apparently has no plural (and/or is the same in the plural, like the English "sheep") and Rahmen is the same (i.e. the words for frame and frames are the same).
So I set out to find similar examples in English, i.e. where:
Word 2 looks like the plural of Word 1, but is not
Word 1 either is its own plural or has no separate plural
Word 2 either is its own plural or has no separate plural
The closest I can find are:
physic (medicinal drugs - apparently it's own plural - or the study of medicine), and physics (the branch of science concerned with the nature and properties of matter and energy, having no plural).
corp (corporation) and corps (body of people). Doesn't quite work as if "corp" is a word, I think it has "corps" as a plural which would break rule 2.
Can you do better?