Even though the question has been answered and accepted long ago, I just want to share my 2 cents.

You can imagine that at the very beginning of your file there is something like (just for explanation):

var module = new Module(...);
var exports = module.exports;

So whatever you do just keep in mind that module.exports and NOT exports will be returned from your module when you're requiring that module from somewhere else.

So when you do something like:

exports.a = function() {
    console.log("a");
}
exports.b = function() {
    console.log("b");
}

You are adding 2 functions a and b to the object to which module.exports points, so the typeof the returning result will be an object : { a: [Function], b: [Function] }

Of course, this is the same result you will get if you are using module.exports in this example instead of exports.

This is the case where you want your module.exports to behave like a container of exported values. Whereas, if you only want to export a constructor function then there is something you should know about using module.exports or exports. Recall that module.exports will be returned when you require something, not exports.

module.exports = function Something() {
    console.log('bla bla');
}

Now typeof returning result is 'function' and you can require it and immediately invoke it like:
var x = require('./file1.js')(); because you overwrite the returning result to be a function.

However, using exports you can't use something like:

exports = function Something() {
    console.log('bla bla');
}
var x = require('./file1.js')(); //Error: require is not a function

Because with exports, the reference no longer points to the object where module.exports points, so there is not a relationship between exports and module.exports anymore. In this case module.exports still points to the empty object {} which will be returned.

The accepted answer from another topic should also help: Does JavaScript pass by reference?

The issue is with

• how ES6 modules are emulated in CommonJS
• how you import the module

ES6 to CommonJS

At the time of writing this, no environment supports ES6 modules natively. When using them in Node.js you need to use something like Babel to convert the modules to CommonJS. But how exactly does that happen?

Many people consider module.exports = ... to be equivalent to export default ... and exports.foo ... to be equivalent to export const foo = .... That's not quite true though, or at least not how Babel does it.

ES6 default exports are actually also named exports, except that default is a "reserved" name and there is special syntax support for it. Lets have a look how Babel compiles named and default exports:

// input
export const foo = 42;
export default 21;

// output
"use strict";

Object.defineProperty(exports, "__esModule", {
  value: true
});
var foo = exports.foo = 42;
exports.default = 21; 

Here we can see that the default export becomes a property on the exports object, just like foo.

Import the module

We can import the module in two ways: Either using CommonJS or using ES6 import syntax.

Your issue: I believe you are doing something like:

var bar = require('./input');
new bar();

expecting that bar is assigned the value of the default export. But as we can see in the example above, the default export is assigned to the default property!

So in order to access the default export we actually have to do

var bar = require('./input').default;

If we use ES6 module syntax, namely

import bar from './input';
console.log(bar);

Babel will transform it to

'use strict';

var _input = require('./input');

var _input2 = _interopRequireDefault(_input);

function _interopRequireDefault(obj) { return obj && obj.__esModule ? obj : { default: obj }; }

console.log(_input2.default);

You can see that every access to bar is converted to access .default.

module.exports is the object that's actually returned as the result of a require call.

The exports variable is initially set to that same object (i.e. it's a shorthand "alias"), so in the module code you would usually write something like this:

let myFunc1 = function() { ... };
let myFunc2 = function() { ... };
exports.myFunc1 = myFunc1;
exports.myFunc2 = myFunc2;

to export (or "expose") the internally scoped functions myFunc1 and myFunc2.

And in the calling code you would use:

const m = require('./mymodule');
m.myFunc1();

where the last line shows how the result of require is (usually) just a plain object whose properties may be accessed.

NB: if you overwrite exports then it will no longer refer to module.exports. So if you wish to assign a new object (or a function reference) to exports then you should also assign that new object to module.exports

It's worth noting that the name added to the exports object does not have to be the same as the module's internally scoped name for the value that you're adding, so you could have:

let myVeryLongInternalName = function() { ... };
exports.shortName = myVeryLongInternalName;
// add other objects, functions, as required

followed by:

const m = require('./mymodule');
m.shortName(); // invokes module.myVeryLongInternalName