What is the exact difference between a 74*374 and a 74*377? The first is classified as an octal edge triggered d-type flipflop while the latter is an 8-bit register. I don't understand the difference between them. Why would one use one over the other?
374 has an output enable, you can make the outputs go high impedance
377 has a clock enable - you can tell the chip to ignore the clock.
As an addition to @Jasen's answer, the main reason behind setting the 74374 outputs to high impedance is to allow you to drive a bus line system without the need for any interface or pull-up components. In other words the high impedance feature allows you to use many 74374 chips with their outputs paralleled. This can not be applied with 74377 chips.
Look at the following picture which has been taken from this link.
I would advice you as well to read the info provided in the already mentioned link.