The correct term for alternate chord shapes is 'inversions'. Often when we see chord boxes written for guitar and the same chord is played in two or more different ways those chords are called versions. The diagram in this post shows two versions of two different chords, both of them 7th chords - the E7 chord and the a minor 7 chord. Each chord has it's own unique sound due to the use of open notes (or not) and the actual sequence in which the notes fall. Let's explore that a little.
The basics of all chords is the Major chord triad. Without getting too far into theory that means we take the first note of a scale, the third note, and the fifth note and play them simultaneously in that order - for example we strum them on guitar or play them simultaneously on a keyboard. Using numbers that is 1,3,5. Players can get creative and change the order of the notes, or create an 'inversion', for example 5,1,3 or 1,5,3. On a guitar a player usually strums through all six strings to create a chord so the sequence might be something like 1,3,5,1,3,1. But, you can see that only three notes are actually used with some being played more than once and in higher or lower pitches. This idea actually works on all non-percussive instruments and even over more than one instrument. For example a bass guitar could play the 1 note and a piano the 3 and 5 notes, together it all adds up to a chord. Ok, we digress, but hopefully that's a few creative ideas for you.
If you're a guitar player and you come across a piece of music that uses an E7 or a min7 chord why not experiment with which version you think sounds best.