Φθόγγος (from the ancient Greek verb φθέγγομαι, to utter a sound) was a sound, any distinct sound, and in Plato it was distinguished from φωνή (voice). In modern Greek it is used to mean any articulate sound.
Φώνημα was a rather rare word in ancient Greek, meaning the sound of a voice, which was used by the French to denote the smallest phonetic unit. It became to phonetics what the atom was to physics.
Ήχος was rare in ancient Greek and is not a term used in linguistics.
It was easy for φώνημα to become phonème in French and phoneme in English, but I don’t think anyone cared much for “phthong” (though they had to swallow diphthong).
In Greek, linguists use φθόγγος to denote ‘a single sound’ as the physical aspect of the phoneme (which is the functional aspect). In a Greek text of linguistics, I would expect to find φθόγγος used for a single articulated sound and φώνημα for phoneme. And vice versa, if I translated from English into Greek, I would translate ‘sound’ as φθόγγος if it referred to human speech.
In your text above, ‘φθόγγος’ is used to mean ‘a single sound’, ‘a phoneme’, to distinguish it from ‘syllable’. In a simple text, not necessarily about phonetics, I would expect to find φθόγγος used instead of φώνημα.