N90 Controller described conflict event between an LGA air carrier go-around and an air carrier departure both operating from Runway 31. Phraseology misunderstanding was listed as a primary factor.

Narrative

Aircraft X was sent around by LGA Tower; Runway 31. As the FLM/Sequencer issued 'runway heading to 4000 FT;' and finals frequency. Tower said they had traffic on the runway; I said 'OK...he's held.' Tower took my OK to mean he was released; without hearing the rest of my sentence; and cleared him for takeoff on Runway 31. My final guy was too busy to turn the go around left and turned him right to give to HAARP for a re sequence to final later. Meanwhile; Aircraft Y departed on a 340 heading. climbing to 5000 FT. I told departure what final was doing with the go around and he turned him to a 90 heading inside the go around aircraft. I believe standard separation was kept throughout; but it was very close. Recommendation; had a chat with the Tower Supervisor on the phone later and explained that is why we don't launch departures after a 'go around.' He understood; but said that the sequence guy there had heard 'OK' and launched him. He called back later to say that from now on they would not release the next departure until they heard the word 'released' from me. Obviously he must have had a conversation with his CPC's about it in-between phone calls. It all seems to go back to the 'heard what you wanted to hear' theory.