A few quick and dirty answers before I go for a bath (I think I stink!)
A microprocessor can do whatever (within reason) you want it to do.
Write some software code to implement a digital clock, connect some kind of a display and voila you have a clock.
Discrete logic chips.
Chip = Integrated Circuit.
Integrated circuit = a device containing lots of transistors and stuff in a small plastic (usually) package with 4, or 8 or 14 or 16 etc "legs" which are the electrical connections.
There are many many types of integrated circuit each of which implements some individual function - amplifier, inverter, AND gate OR gate, counter, shift register, etc, etc.
Bath time!
JimB