ZJX Controller described a loss of separation event in the Non-RADAR environment indicating confusion between the RADAR Controller and the D-Side; one referencing air speed the other altitude.

Narrative

I was working the RADAR position on R52/R51 /(Metta/Knemo/). The URET had a Flight Plan for Aircraft X who was routed over JAINS intersection into ZNY Non-RADAR airspace. ZNY called on the shout line to coordinate an inbound aircraft from Non-RADAR airspace with my sectors. The D-Side answered the line and coordinated the inbound aircraft. While on the line he pulled up the coordination box and coordinated the outbound Aircraft X. We did not have track control of this aircraft at this time; nor was the Data Block flashing to us. Because we were not talking to the aircraft we did not know the MACH number needed for the Non-RADAR coordination. The D-Side coordinated MACH .83 knowing this is a common speed for the L1011. When he got off the line with ZNY he told me the Aircraft X was coordinated and he used MACH .83 for the speed. He said to me when he checks on if the mach number is anything different we will call ZNY back and re coordinate the MACH number. There was never any mention of altitude during this conversation and I believed the final altitude was coordinated at this time. Shortly after; the D-Side was relieved for break. When the data block was flashed to my sector from sector 48 (Georgetown) the aircraft was climbing to FL370; which was the requested final altitude. I had multiple Northbound aircraft at FL370 which were in conflict with the Eastbound Aircraft X. I called Sector 48 and requested they amend Aircraft X's altitude to FL360 for the crossing traffic. Aircraft X remained at FL360 until clear of all crossing traffic; then I cleared the aircraft to cross JAINS at FL370; which was the original final altitude and the altitude I believed had been coordinated. I then terminated RADAR services for Aircraft X and gave the appropriate HF frequency. I was then relieved from the D-side position. He said he had no questions about the sector operations; I went over the traffic; completed a position review and went out on break. When I returned I was made aware of the incident that occurred. The D-Side had coordinated FL330 for Aircraft X with ZNY and I had sent the aircraft out at FL370. Non-RADAR separation was lost with another aircraft in ZNY airspace. When we communicated about the coordination there was never any mention of the altitude coordinated which implied to me that the final altitude was approved; FL330 was never discussed at any point in time. At no time did anyone communicate to me that he/she had noticed any errors displayed in the coordination box. It was later believed that the aircraft was given a T altitude of FL330 by either Sector 48 or ZDC. This is what passed on and appeared in the coordination box when coordination was completed; not the requested final altitude. Recommendation; the recommendation I have to prevent this error in the future would be to change the current altitude section of the coordination box. For our purposes there would be no reason to ever coordinate a 'T' altitude; so there is no reason why this should appear in coordination box. The altitude which should appear should always be whatever altitude is the requested final altitude.