3/8” mechanical pump question

Yup, like that- the barb itself is sized to fit INSIDE of a 3/8 ID hose, so the barb OD is sized a hair over 3/8 (for a snug interference fit into the hose). If you figure a nominal wall thickness (of the barb) of 1/16", that knocks down the ID of the barb section of the fitting to 1/4". Fun, eh?