Just to take this thread further into pedantry, it turns out that the first recorded use of "half-volley" (in 1843) was in reference to cricket (a ball bouncing just reaching before the batsman or fieldsman) So it's possible that both tennis and soccer adopted the term from cricket.
On the other hand the term "volley" goes back to Real Tennis (first recorded use 1596). But it originally referred to the flight of the incoming ball, not the stroke used to hit it (Shots were hit "at the volley" meaning "on the fly.") It appears that the use of "volley" to describe the shot itself comes from the 19th century.
Short hop probably is a baseball term, that's where I've heard it. It was the best equivalent I could think of for the half-volley situation.