Difference between button and switch

Today I had an argument with somebody about the difference between a button and a switch. The button toggles between two states (sound on/off) and changes the icon accordingly. The switch does more or less the same thing (left off/right on).

  1. Is a switch a button in UX terms? In my opinion, the only difference is, that a switch shows the current and also the alternative state while a toggle button only shows the active state (on/off).

  2. What would be a better solution for my scenario above (a game app where you can turn off and on the sound)?

https://developer.apple.com/design/human-interface-guidelines/ios/controls/switches/