F under a hand
Strummed from the lowest string to the highest, this grip sounds F, C, F and A, which are the degrees 1 5 1 3 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 four strings sounding three notes, the 1 appears more than once.
Strummed from the lowest string to the highest, this grip sounds A, F, A and C, which are the degrees 3 1 3 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 3 appears more than once.
Strummed from the lowest string to the highest, this grip sounds C, F and A, which are the degrees 5 1 3 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.
Three shapes for F on ukulele: 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.
A grip that uses only fretted notes, called a closed shape, can slide along the neck. Move it up one fret and every note rises by a semitone, so the chord keeps its quality, major or minor, and changes its name. One closed shape therefore gives you twelve chords, and once you know one of them you can find the other eleven.
Shapes with open strings cannot do this. The open string keeps sounding the same note while everything else moves, so the chord no longer holds together. Open shapes are easier to hold but stay in one place, and closed shapes are harder to hold but can be moved.
On four strings a closed shape often needs only a small barre, with one finger across two or three strings. That is much less work than the six-string version of the same idea, and it is one place where a ukulele is genuinely easier than a guitar rather than simply smaller.