What is the difference between never and void in typescript?

To augment Lee's very good answer, another way to think of it is that in a correctly-typed program, a never value cannot be observed.

In addition to functions which never return (or which always throw exceptions), you'll see the never type when a union type has been exhausted of all its possible constituents:

// Example assumes --strictNullChecks
function fn(x: number | string) {
  if (typeof x === 'number') {
    // x: number in this block
  } else if (typeof x === 'string') {
    // x: string in this block
  } else {
    // x: never in this block
    // this block does not run; the value of x cannot be observed
  }
}

In imperative languages, void can be thought of as a type containing a single value. Such languages do not provide a means to construct or consume this value, but a void function can be thought of as returning this trivial value.

In contrast never is a type containing no values, which means that a function with this return type can never return normally at all. This means either throwing an exception or failing to terminate.