Same subject, two names. A sentence is a piece of language; a proposition is supposed to be the thing a sentence expresses — so that “it is raining” and “il pleut” are two sentences expressing one proposition. Logicians who would rather not commit to propositions existing as objects in their own right say sentential logic, because all they need is sentences and the operations that build new sentences out of old ones. Mathematicians and computer scientists mostly say propositional logic and don't worry about it. Velleman is writing in the logicians' idiom; I grew up in the other one.
The same thing happens one chapter later. Velleman's quantificational logic is what most people call predicate logic, or first-order logic. All three names mean the logic you get when you add ∀ and ∃ to the propositional connectives. If you go looking for other sources — and you should — you will find them filed under the other names.