This exhibit in the museum at Manchester University gave me an opportunity to practise the energy stores language. The display even calls it "stored energy". So pulling the bow, I'd say that the chemical energy store in the human goes down and via the pathway of mechanical work the elastic energy store in the bow goes up a lot whilst the thermal energy store in the surroundings goes up a bit. Then the arrow is fired so the elastic store in the bow goes down and via the pathway of mechanical work the kinetic store in the arrow goes up a lot whilst the thermal store in the surroundings goes up a bit.
