Our resident teachers may have more or better info. Here’s my understanding of the theory:
A chord voicing is the specific notes to play a chord. The same chord played in two different shapes or two locations are different voicings of the chord.
A chord inversion refers to the order of the notes played in the chord, specifically the lowest note. A C chord is CEG. If the lowest note is the root (C) then it is in root position. If the third (E) is the lowest then it’s the 1st inversion, and if the 5th (G) it’s in second inversion.
Position can also mean where your hand is on the fretboard, generally (but not consistently) defined by the fret under your first finger. This is more consistently used in fretless instruments. It’s important more important for violins than ukes.
Playing in different positions up the neck will change both the voicing and the inversion, until you get to the 12th fret when you can repeat the inversions in a higher octave.
Once you learn your way around the fretboard you can choose your chord voicings for effect. Changing voices adds color and allows for deliberate melody or bass lines on top of or under the chord sequence.
Because ukes have only four strings the inversion and position are tied together - on a guitar you can leave strings silent to change the inversion in the same position. This often leads ukelelists to ignore inversion changes that require moving to far as the position change may sound disconcerting even if the voicing is otherwise better.
This also means that if you play the same chord in the same position on a low-G and high-G uke you’ll play different inversions: open-C on a high-G uke is in root position since the lowest note is the C. On the low-G uke it’s a 2nd inversion since the G is lower