Different screw and their material purpose for computers
There are really only 2 factors governing screw use:


Thread pitch/diameter.
Shank length.


There is primarily two threads used in a computer.  There are the "small" ones (M3?) which are used for CDROMs, Floppy drives and (depending on case) sometimes motherboard mounting.

Then there are the larger ones.  These are usually for hard drives, motherboard mounting, and case assembly.

Any others are usually specific to a manufacturer (e.g., special ones to attach a fan to a heat-sink, etc.)

Most of the time the screws are interchangeable within the groupings.  The only thing to watch is the length of the shank.  When screwing into say a hard drive, if the shank is too long there is a good chance it may impact with the circuit on the hard drive and cause damage.

The shape of the head is largely irrelevant, but can sometimes give a good indication of the rest of the screw style at quick glance.  The case assembly / motherboard mounting are usually hexagonal in shape.  These tend to have a longer shank.  The round, flat headed ones in the same pitch are generally shorter, and are used mainly for hard drives.

Often 'special' head shapes/configurations are used to make it easier for machines to assemble the components.

As for materials and colours, well, that's largely down to style and cost.

And washers?  I have never come across anything but insulating paper washers in computers.  Maybe some serrated or split-ring ones in the construction of the case - these are used as non-slip washers that generally go in areas where there may be vibration.  The paper washers are there more for mechanical protection that electrical.  The sponginess prevents over-tightening of the screws and damaging of sensitive circuits.