Lead Technician reported communication issues resulted in logbook errors and a delay to an outbound flight.

Narrative

On Day 1; at approximately XA:30; Crew Chief Person A informed me of the logbook discrepancies on Aircraft X. I signed the Airworthiness Release and stamped the final blocks of the service check for the aircraft; in order to put it into service and make its scheduled flight. I made several mistakes on this release. The first was forgetting to enter the Logbook Deferral Sheet number for Logbook Deferral Sheet XXXXXXX; LH Pack Flow Control Valve repair on compliance page XXXXXXX; which I had crossed out. This I was able to correct when the aircraft returned to ZZZ this morning. The second was for Logbook Deferral Sheet YYYYYYY; compliance page YYYYYYY - flashlight and cradle. For the Aircraft Maintenance Logbook deferral code block; I found it to be blank. Cross-referencing with the Job Card XXXXXX tally and log page job #5; I saw that the item was stamped deferred for parts NIS (Non Incident/Accident Statement) by Crew Chief Person B. I wrote in the deferral code MEL." Crew Chief Person B's turnover to me was that everything on the overnight maintenance was completed except for job #4; LH Pack Flow and job #7; closing of the service check. I then signed the Airworthiness Release and stamped the open blocks on the service check; tally; and the Airworthiness Release complete block on the overnight maintenance accountability report. This resulted in confusion for the Captain of [the] outbound flight; which resulted in a 95-minute delay.There were many factors contributing to my mistakes with the Aircraft Maintenance Logbook of Aircraft X on Day 0. I did not get a lot of sleep the night before. After I badged in at approximately XA:20 I went to the Crew Chief Office to get settled. I customarily ask the night shift crew chiefs if there are any potential turnovers. I find the Crew Chief turnovers to be more accurate; compared to Management's turnovers. Crew Chief Person B informed me that Aircraft X was being turned over with a LH Pack Flow Valve that needed to be worked; with the service check down to final. Then; Crew Chief Person C and I went to Production Control for our workload meeting with Management.We were assigned the following aircraft: Aircraft Y; bleed air fault 3-time repeat item; being worked by holdover overtime AMTs (Aircraft Maintenance Technician); Aircraft Z; LPC bleed and idle run; Aircraft A; Fan Air Valve Thermostat; being worked by holdover overtime AMTs; aircraft X; LH Pack Flow Valve; and Aircraft B; carpet non-routines. The crew was short 3 AMTs; Person D; Person E; and Person F; due to vacations and training. These AMTs were not backfilled. In addition; there was a field trip called for ZZZ1 in which AMTs Person G and Person H accepted. Now we were short 5 full shift AMTs. There was no holdover Crew Chief held in accordance with the JCBA (Joint Collective Bargaining Agreement). Article XX states that when 3 or more AMTs are on shift; that a Crew Chief will be maintained. Article YY states that holdover AMTs shall not be combined to cover known full shift overtime opportunities; but may be held to unplanned maintenance needs. There were 6 AMTs held over for Aircraft Y; Aircraft Z; and Aircraft A in which a holdover Crew Chief could have Lead instead of Crew Chief Person C and I trying [to] manage them; as well as our AMTs and aircraft. We had 3 aircraft to move and stage for Ramp to tow to the gate; and we had to double up on the manning for the crew. In addition; Aircraft B was added to my workload 2 hours after the start of my shift.Avionics was onboard working their items; while I deferred the remaining items. Management kept on coming into the Crew Chief Office asking for continual updates in order to keep updating [the] web-based system. They kept on asking for Aircraft X and when it would be ready to move. I usually do not allow the pressure to get to me but on that day; we were stretched thin and I started to feel the pressure to produce the aircraft. AMTs Person I and Person J were tasked with working Aircraft X; LH Pack Flow Valve. Management kept coming in asking if Aircraft X was ready for Ramp to take it. When the AMTs had successfully repaired the pack flow item; Management again asked if the aircraft can be moved. I replied that it was down to paperwork. Management then asked if Ramp could move the aircraft without the logbook; and that the logbook would be delivered afterward. This is a common occurrence at ZZZ; moving an aircraft without a logbook. There have been occasions where Ramp has moved an aircraft without approval from Maintenance. In this case; I relented and gave my approval for Aircraft X to be moved to the gate while the AMTs were completing their paperwork. The AMTs signed off their item in the logbook; Logbook Deferral Sheet XXXXXXX; non-routines; and job card #4. However; they did not enter their item into [the system]; nor did they call Maintenance Control to unlock the item so it can be cleared. I called Maintenance Control on their behalf and entered their item into [the system]. I was rushing; and this is where I forgot to write the Logbook Deferral Sheet number into the Aircraft Maintenance Logbook; on compliance page XXXXXXX.By now; Aircraft X was on the gate and the flight crew was asking for the logbook. Crew Chief Person K called me asking for the logbook; which was not ready yet. I briefly looked at the other sign-offs in the Aircraft Maintenance Logbook for Logbook Deferral Sheet YYYYYYY; compliance page YYYYYYY; and saw that the deferral code block was blank. This is where I quickly cross-referenced the Job Card XXXXXX tally and saw that job #5; Logbook Deferral Sheet YYYYYYY; was deferred. I checked the job card itself and saw that it was deferred for parts NIS at ZZZ. This is when I wrote in the deferral code "MEL" to correspond with the tally and job cards. The sign-off was confusing in the logbook and did not match the job card. It seemed to say something about 2 placards. The sign-off did not make sense. However; the tally showed 2 items deferred; job cards 5 and 6 were deferred; and there were 2 placards in the logbook. The placards were for "1L OTBD Flashlight INOP" and "L2 OTBD Seat INOP due to INOP flashlight." These were previous deferrals that apparently were not repaired. In the rush to produce the logbook for a timely departure; as well as managing the other aircraft; with a short-staffed day shift crew; as well as having to manage overtime AMTs; I failed to look into the confusing verbiage deeper. Signed off the Airworthiness Release; and Crew Chief Person C took the logbook down to the aircraft. Afterward; Crew Chief Person A was called out to the aircraft because the Captain was confused with the logbook. This occurred after I had ended my shift. Crew Chief Person A was also confused by the sign-off in the Aircraft Maintenance Logbook for Logbook Deferral Sheet YYYYYYY. He tried to sort it out and was under pressure because the crew was going to time out. He believed that amt name1 had forgotten to sign off Logbook Deferral Sheet ZZZZZZZ; if I understood him correctly; and transcribed his sign-off for Logbook Deferral Sheet YYYYYYY to ZZZZZZZ. Person A had no time to retrieve the pack from the hangar; before the crew timed out. The next morning Crew Chief Person A informed me of the events that transpired at the gate concerning Aircraft X's Aircraft Maintenance Logbook.The first thing that I must do is to pace myself and not give into pressure from Management. I should insist that Ramp not be allowed to move aircraft to the gate without the Aircraft Maintenance Logbook first being adequately reviewed; released for service; and placed on the aircraft. I should also insist on Management holding over an overtime Crew Chief for overtime AMTs. I need to make sure that I understand what has been written in the Aircraft Maintenance Logbook and if there are discrepancies; to not give into pressure and release the aircraft for service."