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I would say they are the same thing. Different ways of saying the same thing. Which in fact, is what inversions are!
Technically to 'invert' a chord you take the lowest note up an octave so it becomes the highest. e.g 1,3,5 becomes 3,5,1 which inverts to become 5,1,3.
In an actual musical situation you might VOICE a chord so that some of those notes are spread across several octaves, some notes are doubled an octave above or below (or in unison, on a guitar for instance, though this is rare).
'Voicing' could also include things like drop 2 and 3 chords, closed vs. open (more than one octave).
In short, inversions happen mainly on paper and in theory exams and refer to a very specific re-ordering of the notes in a chord. Voicings happen on your instrument and cover just about everything you could do to that chord. They are similar, but there is a subtle difference.