What are half steps and whole steps?
The two smallest distances between notes. A half step is the jump to the very next key — piano or fret; a whole step is two of those, skipping the key in between. are just patterns of these.
A half step (or semitone) is the smallest move in Western music: from any key to the one immediately beside it, black or white. A whole step (or whole tone) is two half steps stacked, so you skip the key in between. Both are distances between notes, not kinds of note — every key is a full note, so an octave holds twelve notes and twelve half steps, and 'whole' just means the larger of the two common step sizes. (The similar-sounding whole note and half note are rhythm terms for how long a note lasts.) Every scale is a recipe written in these two distances — the major scale, for instance, runs whole–whole–half–whole–whole–whole–half. The catch is on the white keys: most neighbours are a whole step apart, but E–F and B–C are half steps with no black key between them, which is exactly why the piano is laid out the way it is.
Play it
A half step is the jump to the very next key — C → C♯. A whole step skips one key — C → D. Press any two neighbouring keys to hear a half step, or skip one for a whole step. Notice E–F and B–C are half steps too, even with no black key between them.