Actually, if I can be allowed to be a little pedantic, if we're just talking about the notes of a chord, two chords aren't really "inversions" of one another even if they have the same notes, because the term "inversion" refers to particular voicings and not just the notes.

So, "C E G", "E G C", and "G C E" are all inversions of a C triad, but not "C G E", because of the gap between the C and the G, where an E would fit. Many chords on a guitar are not inversions in the sense of a voicing produced by means of a procedure where one takes a chord in "closed position" with the root in the bass, removes the bass note, replaces it with the same note an octave above, and then does the same thing for each successive bass note until one has the original voicing, an octave higher.