I just did a bit of research into this myself. I have only a small amount of experience in the pump field, but here is what I have to offer:
There are two basic methods of transferring power from a motor to a pump. A for a close (not closed) coupled pump, the impeller (or gearbox, in your case) is mounted directly to the motor's output shaft, and the bearings of both items are affected by loads applied to either the motor or impeller. The motor is typically mounted directly the the pump volute, requiring a face-mounted motor type. This is also a standard method of attaching motors to gearboxes. Because everything is on a common shaft, there are fewer issues with misalignment, but routine maintenance may require disassembly of the pump.
On a long coupled pump, the pump shaft and motor shaft are separate components, with power transferred by a coupler. The motor is typically a base-mount type and each component (pump and motor) have separate bearing assemblies. This prevents transmission of thrust and radial loads between the two shafts. Alignment is critical, but is easily accomplished by a good technician. Maintenance is simpler because either pump or motor may be replaced without disturbing the other.
One note: a motor, by itself, is not close coupled. Close couple describes the connection of the motor to the driven equipment. No connection, no couple.
Based on what you've described, I assume you have a face mount motor coupled to a gearbox and are considering replacement of the gearbox. This is not a big deal, but the new gearbox must accept the frame/face configuration of the existing motor. Most NEMA face mount motors include a "C" in the frame size (145TC, 56C, etc.). Match those numbers with your motor-gearbox and you should be OK.
Dylan Christopherson, PE