How does propositional logic differ from predicate logic?

Propositional logic and predicate logic differ primarily in their level of analysis and the atomic units they employ.

Propositional Logic
Also known as the propositional calculus, this system treats propositions as atomic, unanalyzed units. It focuses on how complex statements are constructed from simpler ones using logical connectives such as "and," "or," and "if...then." These connectives are truth-functional, meaning the truth-value of a complex statement is determined entirely by the truth-values of its component parts, a relationship often visualized using truth tables.1

Predicate Logic
In contrast, predicate logic (or predicate calculus) analyzes the internal structure of propositions by breaking them down into predicates and nouns (or arguments). Its most significant feature is the use of quantifiers—specifically the universal quantifier ($\forall x$) and the existential quantifier ($\exists x$)—which allow for the expression of generalizations like "everything is" or "something is." While propositional logic deals with whole statements, predicate logic examines properties, relations, and the individuals within a "universe of discourse," providing a more granular framework for logical analysis.12