This is not how to play to play them but what you call them. As E shaped barre chord 6th string root, they are the same notes, the chords not just the notes are enharmonic equivalents, I think is the term.
I presume it is all to do with chords in the key and the circle of fifths, see Richard’s diagram, from his posts on C of 5ths
It is wholly context, convention and usage driven Michael.
During my Vintage Club session this week I showed an exercise of descending major barre chords from fret 6 to fret 1.
Because the first chord I named B flat major, I made an aside that we were in the world of flats so called the chords Bb, A, Ab, G, Gb, F.
It is not that the key of B flat co tains all of those notes - no key contains six chromatic notes - but that it does contain flats and no sharps.
If you were playing a diatonic progression in the key of A major, the E-shape barre chord at fret 4 must be called G# and not Ab. The key of A contains sharps not flats and the letter A cannot be used more than once.
Which name you use depends on the key of the music that you are talking about.
Since, by convention, every LETTER should only be used once to describe the notes in the key, you choose whichever enharmonic name that allows each letter only once in the key.
For example, the G major key is made up of G, A, B, C, D, E, and F#. You use F# instead of Gb so there won’t be two G’s in the key description.
If I pick up on that specific, chromatic sequence of chords again. They are not all diatonic to any key. If they were analysed as a progression from a piece of music (not some sequential exercise) then we would need to describe things calling upon borrowed chords.
If Bb is the tonic chord …
The chords in the key of B flat major are:
Bb = I
Cm = ii
Dm = iii
Eb = IV
F = V
Gm = vi
Adim = vii
The progression:
| Bb | A | Ab | G | Gb | F |
| I | VII | bVII | VI | bVI | IV |
Only the I and the IV chords are diatonic, all others are borrowed and given a Roman numeral value referenced back to the letter names of A or G. The Roman numeral designations all take ‘flat’.
If F is the tonic chord …
The chords in the key of F major are:
F = I
Gm = ii
Am = iii
Bb = IV
C = V
Dm = vi
Edim = vii
The progression:
| Bb | A | Ab | G | Gb | F |
| IV | III | bIII | II | bII | I |
Only the IV and the I chords are diatonic, all others are borrowed and given a Roman numeral value referenced back to the letter names of A or G. The Roman numeral designations all take ‘flat’ here too.
The keys of B flat and F both contain at least one flat (plus natural notes). When ‘out of key’ chords are added to a progression in those keys, the naming conventions mean that ‘flat’ is used for these visitors too.