I was wondering if all three of these terms: chromatic, non-diatonic, accidental, all mean the same thing?
The three terms may refer to the same note in a piece but they do not really mean the same thing.
Chromatic refers to out-of-scale half-step movement. For example F to F# in the key of C or to notes that are not within that scale. Chromatic may refer to several notes in a row, C-C#-D-D#-E for example.
Non-diatonic generally refers to notes not in a given major key. The term isn't quite as useful in a minor key piece as the 6th and 7th scale steps are mutable and both versions are often referred to as diatonic (leaving only two notes as non-diatonic in even-temperament).
Accidental refers to the flat or sharp sign attached to a note. A note with such a sign may be called an accidental for short. However, such a note may be diatonic as in the key of D-major, one might have an F-natural followed by an F# (no natural sign on my character set.) Both notes have an accidental applied.
Diatonic - belonging to a specific key - as in those notes played in a scale in that key.
Non-diatonic - any other notes which are not diatonic! As in they are not part of the set of notes which constitute a specific key.
Accidental - a sign which changes a note from the original, but retains the same letter name, E.g. B♭ appearing in the key C. It's non-diatonic, so the B gets changed with an accidental into B♭; F ♯ appearing in the key C. It's non-diatonic, so the F gets changed into F♯; Bnat. needs a natural sign in the key F, as diatonically, there's B♭. On certain occasions, ♭♭ and x are used to denote doule flat and double sharp. They also are know as accidentals.
Chromatic - any note which is non-diatonic, and will need an accidental sign to qualify it in a key.
Note (!) the signs at the beginning of a piece which we call the key signature are not accidentals - they're there on purpose! Called - the key signature.
Accidentals are signs as flats (b) and sharps (#) usued for alteration of the tone pitch, also the sign for a natural tone. The altered notes may also be called accidentals.
Non-diatonic are the tones that are outside of a given scheme (scale) of whole tone - and half tone steps. Sometimes they can be identified by the accidentals.
The chromatic scale consists of 12 half tone steps. Notes that don’t belong to a defined scale are chromatic.
Altered tones, notes with accidentals, can be chromatic tones or non-diatonic or both. The term “chromatic” describes the new color given by an alteration.
The more I know ... the more I know that I know nothing!