Actually, the different between fuzzy logic and probability is more than just notational. There is a nice table at the end of Section 8.2 (in the 3rd edition) of Russell and Norvig's Artificial Intelligence book talking about the epistemological (what an intelligent agent believe about facts) versus ontological commitments (what exists in the world) of various "languages" (e.g., propositional logic, first-order logic, probability theory and fuzzy logic).

Taken straight from that table, here is the comparison:

Language | Ontological Commitment | Epistemological commitment

Probability | facts | Degree of belief \in range from 0 to 1

Fuzzy Logic | facts with degree of truth | known interval value