I like to think of a switch as a type of toggle button: it's a button that can be in two states, denoting "on" and "off". It behaves pretty much exactly like a regular button.
Another way of looking at it would be seeing a switch as a type of checkbox: it is a control that can be "on" or "off" (and sometimes "none"), displaying the current state to the user.
Lately they try to separate those two, though, because they play different roles: a checkbox is being used more as a way to select something from the list, while switch - to turn something on or off.
I like this article on the topic, which pretty much summarises the difference:
A checkbox control has three states: unselected, selected, and
indeterminate. The last state represents a situation where a list of
sub-options is grouped under a parent option and sub-options are in
both selected and unselected states.
A toggle switch represents a physical switch that allows users to turn
things on or off, like a light switch.
Tapping a toggle switch is a two-step action: selection and execution,
whereas checkbox is just selection of an option and its execution
usually requires another control.
Moreover, Material guidelines call switches "buttons" and even are being inherited from buttons (which basically means, everything a button can do, a switch can do too). That should settle it.
Now, for your second question.
If you have to choose between using a toggle button or a switch for turning the sound on and off, you should consider if it will be clear for user what that control would do when pressed.
If there's only one control on the screen, you should probably go with the switch: it's more clear that you can turn something on and off with it. The toggle button is usually undistinguishable from a regular button and there's no way for a user to know what happens when they press it, especially if there are no other clues around - will it toggle, or, for example, open a popup?
This usually isn't that much of a problem, but something to consider nonetheless.
