module.exports vs. export default in Node.js and ES6

What is the difference between Node’s module.exports and ES6’s export default? I’m trying to figure out why I get the “__ is not a constructor” error when I try to export default in Node.js 6.2.2.

What works

'use strict'
class SlimShady {
  constructor(options) {
    this._options = options
  }

  sayName() {
    return 'My name is Slim Shady.'
  }
}

// This works
module.exports = SlimShady

What doesn’t work

'use strict'
class SlimShady {
  constructor(options) {
    this._options = options
  }

  sayName() {
    return 'My name is Slim Shady.'
  }
}

// This will cause the "SlimShady is not a constructor" error
// if in another file I try `let marshall = new SlimShady()`
export default SlimShady