Yes. Your use of the term diatonic is correct.
You can describe the collection of tones and their intervallic relations in several ways. It's common to describe diatonic as the tones of a major scale.
Recently, I have been thinking of it as the collection of pitch classes you get from six ascending perfect fifths. That doesn't necessarily define a tonic and is "scale agnostic." Those tones could be rearranged into a major scale, Dorian mode, etc.
There is another view that extends that 7 tone notion of diatonicism which says roughly the 12 tone chromatic scale with emphasis on those 7 tones is diatonicism. Personally, that seems circular: if those 7 tones are what makes the distinction, it's simpler to just refer to those 7 tones.
As for the first comment, I think it started with a sarcastic tone that wasn't helpful. In English "diatonic" is an adjective. If you want to use the concept as a noun, the subject of a sentence, you use "diatonicism." Word endings "-ic" and "-ism" modify root words. Compare that with "Catholic" (adjective) and "Catholicism" (a noun.) "-ism" noun forms get used for ideas like religion or art movements, ex. "Cubism." In fact, "ism(s)" is a word in English (deragatory tone) referring to ideologies or philosophies. So, the comments was apparently trying to make a joke, a play on words. Unfortunately, I think the comment had the tone of mocking the question or the notion of diatonicism as a legitimate musical term.
As for the second comment, I think the important part was "...a misunderstood concept by students..." Some people have this strange misunderstanding that classical harmony is diatonic. Literally using only the tones or a key signature an no chromatic tones. The only person who could have that misunderstanding is someone who has spend almost no time reading actual classical scores or someone who stopped reading their harmony textbook after the first few chapters.
We don't need a better word for the concept, because these are standard terminology. Some examples of usage in Grove's Online:
- "Based on or derivable from an octave of seven notes in a particular configuration, as opposed to Chromatic and other forms of Scale. A seven-note scale is said to be diatonic when its octave span is filled by five tones and two semitones..."
- "Based on an octave of 12 semitones, as opposed to a seven-note Diatonic scale."
- "It may be true to the diatonicism of the passage..."
...would you say that harmonic minor is diatonic ?
It seems like old definitions use the Medieval gamut (in modern terms, roughly the major and minor key signatures) as the definition of diatonic. The few I could find at Google books don't make reference to minor specifically.
More modern definitions break out a definition for minor and say the various forms of minor scale (raised or lowered sixth & seventh degree) are considered diatonic.
Personally, I like the old view that diatonic is the Medieval gamut.
I think most people would refer to the raised seventh in minor as a chromatic tone, because it's altered from the key signature. But when putting the question into a context of scale or chords of the key, people then want to call it diatonic. That makes diatonic have the practical meaning of belonging to the key.
I don't think you will escape that dual meaning. People seem to flip back and forth depending on the musical context. The sort of default meaning is the 7 tones of the modes, but when the context is minor key it includes the raised sixth and seventh for 9 tones.
One final thought: I wondered why do people feel the need to fit raised sixth and seventh into a definition of diatonic? That made me realize another important connotation of diatonic. The old view was diatonic tones are natural. Natural in the sense of proper and good. Notice then the application of that notion in natural minor, it's the minor scale form that conforms to the Medieval gamut. I guess some people needed to classify the raised sixth and seventh in minor as diatonic so those tones too could have the status of natural, just as proper and good as the other tones.