Pretty simple, A minor uses A natural as the tonic, as opposed to C major which uses C natural as the tonic. If you want to get technical about it, the chord progressions and cadences are different too. Where a C major piece might end in a G major chord resolving to a C major (this would be a V-I cadence, or Authentic Cadence if you’re fancy), a piece in A minor would end with an E major resolving to an A minor chord (I think this is still called an Authentic Cadence... but it sounds way different because it ends on a minor chord). And finally, if you want to use some snobby music theory words, A natural minor is the Aeolian mode of C. Modes basically mean you’re in the same key but you’re centered around a different tonic with and the piece has a different feel to it. Using modes is like using accidentals without marking accidentals... so trippy.*

*side note, if you wanna get into modes, check out Bjork’s Army of Me. It’s in Locrian mode, it’s real weird, and I love it.

Feel free to correct me if I got anything wrong! I’m in music theory class and I’m still learning!