Let's make the distinction between "shape notes" as in notation, and "shape note" as a singing style.
"Shaped note" notation was developed to facilitate sight singing in an often non-literate culture. Simple geometric shapes were assigned to the steps of the scale as a visual cue. The earliest shape note systems were "four note" [or four shape]. Instead of do-re-mi, etc. [and don't ask me why, I'm shootin' from the hip here- being too lazy to look it all up again]the major scale steps were fa so la fa so la mi fa [tho' it sounded just like the do re mi]. Out of several tunebook compilers' efforts, the most widely-used system that emerged/endured labeled a triangle as "fa", a circle as "so", a square as "la", and a diamond as "mi" [the leading tone of the scale]. This is the system used in both the Southern Harmony and the Sacred Harp [1844] tunebooks.
Before someone asks "why didn't they just go by the lines and spaces like I did in piano lessons", please remember that lines/spaces are a part of the "fixed do" or maybe I should say "fixed tonic" [fixed fa?]notation that instrumentalists use- tied to even temperament, etc. Shape notes were developed to aid singers, and unaccompanied ones, at that; so they use/d "moveable do [tonic, fa, etc]". In other words, as long as the pitches are in the same relationship to each other, [and we can hit the pitch]we really don't care whether it's a D or an F. [I confess that I don't know of any well-adjusted Sacred Harp singers with perfect pitch- 'bless their hearts!]
So, then, in the middle of the 19th century, someone came along with a "new and improved" notation system featuring seven shapes [aka seven-note]and the do-re-mi scale. Many of the tunes from the earlier four-note books were now transcribed into seven-note notation. The Christian Harmony tunebook uses this system. The seven shape system found its way into other realms of vocal music: As congregations began to use the camp-meeting revival-type songs in their services, even with accompaniment now, shape notes continued to be used [on a closed score though]. This is the beginning of what eventually became known as "gospel" or "Stamps-Baxter" [so named after one of the most successful publishers of this genre] or even "new book" [to distinguish it from the unaccompanied four-note] singing.
[How well I remember my Daddy's reaction to our church's purchase of "round note" hymnals in the 60s- it was just another sign of the end times!! ;o)]
I am not going to get into the term "gospel" as applied to a genre of music; and I don't really want to get into this tradition or that tradition. I will say that even among four-note singers, you find a variety of regional styles- even when they're singing from the same book. The same kind of thing pops up among fiddlers from either Cork or Clare. So there! T