Melodic movement to an adjacent pitch in a [musical] scale.
The size of adjacent degrees of a scale.
In equal temperaments, all steps are the same size, but in Just Intonation, this is almost never true.
Chalmers's statement that "in equal temperaments, all steps are the same size" refers to the steps between each degree of an ET. In most diatonic scales, steps typically come in two sizes, which may be denoted L and s, for "large" and "small" respectively.
These are typically called "whole-step" and "half-step" respectively, but this logarithmic ratio is mathematically exact only in 12-edo, and not in any other tuning of the diatonic scales (specifically referring to other tunings of the meantone family) -- thus, the "whole/half" terminology is used only in a general sense in those other tunings. For example (in fact, the most extreme example), in 19-edo, which divides the whole-tone into 3 equal parts, a "half-step" can be either 1/3 of a tone (the "chromatic-semitone") or 2/3 of a tone (the "diatonic-semitone").