What is an example of driver and receiver chips for a PCB?
In digital logic, a driver is just a buffer (a gate whose output is the same as its input) designed to produce a relatively high output current, so that it can deliver a signal across a relatively long (and high capacitance) trace. For example, a 74LVC244 chip is often described as a "buffer/driver" chip.

A receiver is a buffer designed to be able to fully switch its output with a relatively low amplitude input signal. You won't find too many chips sold specifically as receivers, but there are several that are called transceivers, combining driver and receiver functions.

Generically, your instructor might just be using these terms to mean whatever gate drives a signal onto a line and whatever gate receives the signal from the line.