What are the different progressions using chords built on the 1st, 4th, 5th, and 6th notes of a major or minor scale called?

The term that best describes the different progressions using chords built on the 1st, 4th, 5th, and 6th notes of a major or minor scale is "Chord Progressions." These are sequences of chords played in a particular order and are fundamental to the structure of much music. The 1st (tonic), 4th (subdominant), and 5th (dominant) chords are especially important in Western music theory, forming the basis of many popular progressions, often referred to using Roman numeral analysis.

While "harmonic structures" may suggest a broader range of chord relationships, the specific focus on the ordered sequences that define a piece's harmonic framework is more accurately represented by the term chord progressions. "Melodic lines" refer to sequences of notes that create a melody, while "rhythmic patterns" deal with the organization of time in music—neither of which pertains directly to the concept of chord progressions. Therefore, chord progressions are the correct terminology for this specific concept in music theory.