Alternative voicings, where you play the chord at different positions on the fretboard to get different sounds, are very useful, and have already been explained.

Alternative fingerings, where you play that voicing using different fingerings from whatever your teacher or course recommends, are also very useful. Their main use is in making it easier to transition smoothly from the current chord to the next. As an example, take C to G7 at the root (0003 to 0212). If you fret the C chord with your third finger you have to slide that finger down to make the G7 using fingers 1, 2, 3 - that doesn't make a clean transition. But if you fret the C chord with your 4th (pinkie) finger, it's much easier.

One other thing to think about is whether you can make a chord change without moving one finger (often called anchoring that finger). That can really help with slick changes. Take, say, the sequence C, Am, F, all at the root position. If you finger the C (0003) with your 4th (pinkie), then you can play the Am as 2003 (keeping that pinkie in place), and then the F as 2013 (again, the pinkie stays). As it happens, these are also better fingerings for the Am and F than 2000 and 2010 because you don't double the A note at the same pitch.

Which fingering to use depends where you are going next. Suppose your sequence is C, Am7. If you are playing it as 0003, 0000 then it doesn't matter which finger you use for the C. But if you are playing the Am7 as 0453, then it's easiest to use finger 1 to play the C. And so on ..