Where I'm from (Britain), we call a half-step a semitone and a whole-step a whole tone, so bear with me.
The difference between a semitone and a whole tone is that a semitone is the shortest distance you can play two keys (for example F# to G or B to C).
However, a whole tone is two semitones. It's the difference between two keys that are the same type (e.g. F# to G# or C to D) - (black to black or white to white).
A half-step is the note that doesn't have other keys in between. There are Black keys and White keys so if you go from the e note to an f note that is a Half Note
If you go from an a note to a b note you have a Whole note this is because there are notes in between it.
