Terms:
semitone
half-step
diatonic
chromatic
diatonic half-step
chromatic half-step
enharmonic
enharmonic equivalent
natural half-step
whole-step
The difference in pitch between two adjacent keys on the keyboard is an interval called a semitone, or less formally, a half-step. There are twelve half-steps to an octave. Theorists recognize two types of half-steps which are called diatonic half-steps and chromatic half-steps.
The type and notation of a half-step are determined by the names given to the notes it comprises. To illustrate, let’s consider a half-step from a white key up to a black key. As you have already learned, black keys are named relative to a neighboring white key using an accidental. Thus, the black key above G can be called G-sharp (relating it to the white key below) or A-flat (relating it to the white key above). G to G-sharp and G to A-flat are both half-steps, but each is of a different type. G to G-sharp is considered to be a chromatic half-step because the two notes share the same letter-name; G to A-flat is considered to be a diatonic half-step because the two notes have different letter-names. Note also that the two half-steps would be played exactly the same way on the keyboard and would also sound exactly the same despite the different spellings. As you have already learned in the lessons about accidentals, a relationship of this sort is referred to as enharmonic. In this example, the two half-steps are considered to be enharmonic equivalents.
You have probably noticed that, in addition to the half-steps between white and black keys, the keyboard includes half-steps between some pairs of white keys, i.e. the white key pairs E-F and B-C. These are diatonic half-steps, of course, but since no accidentals are required to spell them, they are also referred to as “natural” half-steps. Be aware, however, that even the natural half-steps can be enharmonically spelled or notated using accidentals. For example, the half-step from E to F could be enharmonically spelled or notated as E to E-sharp or as F-flat to F. In either case it would sound and be played exactly the same way.