How did Leibniz’s intensional logic differ from a logic based on classes of objects?

Gottfried Wilhelm Leibniz’s logical system was fundamentally intensional, meaning its terms stood for properties or concepts rather than for the individual objects that possess those properties.1

In contrast, a logic based on classes of objects is extensional. In extensional logic, the reference of a term is determined by its extension—the range of particular objects that the term denotes.12

The primary differences are:

• Focus of Terms: Leibniz’s intensional logic treated terms as collections or conjunctions of basic concepts. For Leibniz, the truth of a judgment was defined by the inclusion of concepts: a predicate was considered "included in" the concept of the subject. Conversely, extensional logic focuses on the set of individuals that fall under a concept.12
• Symbolic Representation: When Leibniz used symbols to represent relationships, such as $A=B$, he was asserting that the concepts making up concept $A$ are contained in concept $B$, and vice versa. In a class-based (extensional) system, such an equation would instead signify that the two terms denote the exact same collection of individual objects.12

Leibniz’s approach reflected his goal of creating a "calculus of reason" based on the internal structure of concepts.1