That is actually the way I think of notes in tonal music: You've got a root, a second, a third, … , a sixth and a seventh. But there are different kinds of each degree of the scale (apart from the root): the second could be minor or major or augmented (`sharp 9' is jazz lingo); the third could be major or minor etc.
But you don't have to choose just one type of third or fifth etc. in a given piece of music (or part thereof). You can have a single melodic phrase that uses both the major and the minor third, but I think of these as two different `inflections' of the same degree of the scale, the third.
Likewise, you can have a chord that contains more than one version of the same degree of the scale. In the chord E7#9 (E, G#, B, D, F##) the G on the top is being described as F##, but what I hear is two different versions of the third (major and minor) simultaneously.
Blues music certainly thinks in this way. When a blues musician bends around on the third or fourth, it's all the one note, but `inflecting' or `embelishing' that note.