What is the difference between working height, tower height and platform height?

This needs to be answered in reverse.

The Platform height is how far you are standing off the floor, that is, distance between the ground and the upper platform board.

The Tower height is the physical height of the tower itself, that is, distance between the ground and the top rail.

The working height is how high you can reach when you are standing on the platform. It is a common practice that working height is platform height plus 2 metres.

Please see Height Specification for a handy diagram below.