FWIW I had understood puns to be jokes based on two words with different meanings that sounded similar but were not identical, such as the example above "I never sausage a thing." A play on words uses actual dual meanings, and I somehow had understood to be a little higher than a pun. For example, "In preparation for the party, Doris watered the flowers, and David, the drinks." This uses two slightly different meanings of the verb "to water." (Or at least slightly different motivations for pouring water.) In comparison, the question "Water you looking at?" is a pun because it relies on the phonetic similarity between "what are" and "water." In short, puns are wordplay based primarily on the way words sound and nothing more. More sophisticated wordplay involves invoking dual meanings from a single word.

That said, the actual dictionary definition of a pun is broader than I had believed and does include wordplay in general.