Air carrier Captain reported a mechanic brought the wrong logbook to the aircraft and another mechanic subsequently brought the correct logbook.

Narrative

Early morning departure. Show up to plane. No logbook. Continue to load box; set up for flight etc... aprox 20 min before departure Maintenance Technician shows up and hands us the logbook. Only problem- it was the wrong logbook. I caught this error and called the Mechanic back. I explained to him this could have been a huge mistake if it this error was not trapped. He told us they were over worked; too many planes on the ground; too many jobs to do with not enough staff; and he was told to deliver it to Gate XX where we were located. The plane he was actually looking for was on Gate XY. He didn't seem to get the message that no matter how rushed he felt; he needed to slow down and do proper work and not take short cuts. He leaves.New Mechanic comes to the plane with our actual Aircraft Logbook; and he repeats the same complaints that the first Mechanic had. They have more planes on the ground each night with more work orders than mechanics to do them. He also said they were pressured by supervisors to get work done even though they feel rushed and make mistakes because of it.As a Pilot who flies into ZZZ quite often; this is now becoming our problem too. I'm not a fan of mechanics taking short cuts because they are being pressured to complete or sign off unsatisfactory work. This should be a red flag to the safety department to start some digging into the maintenance technicians operation in ZZZ.Fun fact: the only other time I've had the wrong logbook delivered to the plane was also in ZZZ. [Cause is] Rushing of maintenance technician personnel. Look into ZZZ maintenance technicians.