What is the difference between function foo(){} and foo: function(){} in Javascript?

You can write function in two ways: as named function or as variable that has value as anonymous function:

var fooBoo = function () {};
function fooBoo(){}

Calling it is the same: fooBoo().

From your example it seems that you have object with one of keys with function:

var myObj = {
 fooBar: function () {}
}

Now in this situation you can't replace it with function fooBar(){} as it would end up in wrong syntax:

// NOT VALID!
var myObj = {
 function fooBar() {}
}

It is an object property declaration:

const thing = {
 clickNext: function(e) {
 ...
 }
}

thing.clickNext()

It's same object literal syntax as:

const person = {
 name: "Jane",
 age: 33
}

They are not the same things.

// this cannot be in itself
clickNext: function(e) {
 var cal = $(e.target).parents('.drp-calendar');
 if (cal.hasClass('left')) {
 this.leftCalendar.month.add(1, 'month');
 } else {
 this.rightCalendar.month.add(1, 'month');
 if (this.linkedCalendars)
 this.leftCalendar.month.add(1, 'month');
 }
 this.updateCalendars();
},

This is part of an `Object, like:

const obj = {
 value1: 5,
 clickNext: function(e) {
 console.log(`${e} is your function`)
 },
 value2: [0, 1, 2, 3, 4, 5]
}
obj.clickNext('this')

This is a function in itself:

// no comma at the end!!!
function clickNext(e) {
 console.log(`${e} is your function`)
}
clickNext('this')

Below is an example of declaring functions in JavaScript, it is known as Function declaration. Keys points to note:

• We call this function as function name followed by paranthesis - clickNext().

• this keyword refers to global object inside function declaration, which means it refers to window object.

  function clickNext() { console.log(this) // this refers to global object window here. }

Below is an example of methods. When we have a function inside an object, it is called as method.

• We call a method using syntax of - dummyObject.clickNext()

• this keyword refers to object in which it is declared which means in below example this refers to dummyObject.

  const dummyObject = { clickNext: function(e) { console.log(this) // this refers to dummyObject here } };

• javascript