F under a hand
Strummed from the lowest string to the highest, this grip sounds F, C, F, A, C and F, which are the degrees 1 5 1 3 5 1 rather than the 1 3 5 of the written chord. The root is the lowest note, so this grip is in root position and sounds the way the written chord suggests. With F in the bass and six strings sounding three notes, the 1 and 5 appear more than once.
Strummed from the lowest string to the highest, this grip sounds A, C, F and C, which are the degrees 3 5 1 5 rather than the 1 3 5 of the written chord. The lowest note is the 3 rather than the root, so this grip is in first inversion, written F/A. It has the same notes as the root-position grip, but with A in the bass it sounds different. With A in the bass and four strings sounding three notes, the 5 appears more than once.
Strummed from the lowest string to the highest, this grip sounds C, F, C, F, A and C, which are the degrees 5 1 5 1 3 5 rather than the 1 3 5 of the written chord. The lowest note is the 5 rather than the root, so this grip is in second inversion, written F/C. It has the same notes as the root-position grip, but with C in the bass it sounds different. With C in the bass and six strings sounding three notes, the 1 and 5 appear more than once.
Three shapes for F on guitar: F, F/A and F/C.
Every grip here is F, but no two of them sound alike. A chord with the root as its lowest note is in root position, and a chord with any other note at the bottom is an inversion. On a keyboard you choose the inversion you want, but on a neck the shape your hand can reach usually decides it for you. When a grip sounds a note more than once, the fretting hand decides which note that is, not the harmony.
The nut does the job of a finger holding down every string at once. If you lay your index finger across all the strings at the first fret, you have moved the nut up a semitone. Play the open E shape above that finger and you are playing F.
That is a barre chord, and it is why guitarists learn shapes rather than individual chords. The E shape gives a major chord with its root on the sixth string, and the A shape gives one with its root on the fifth. With these two shapes and twelve frets, you can play every major chord.
F is the E shape at fret 1 and the A shape at fret 8. Both contain the same three notes, arranged differently, so they sound different. Both are equally correct ways to play F.