What's the difference between objects and associated array in javascript?

Not really, here's why:

var arr = new Array();
arr["foo"] = 100;
arr["bar"] = 200;
console.log(arr.length); // Prints 0.

Adding elements to an associative array should increase its length (IMO).

It looks and acts (somewhat) like an associative array because of syntactic sugar. What appear to be "array entries", however, are (just) object properties.

If you define "associative array" as a data structure that stores information as a collection of key-value pairs, then yes, JavaScript objects are associative arrays.

However, the phrase "associative array" is not generally used in the context of JavaScript, rather, we say "object". I'd suggest sticking to standard JS terminology to avoid misunderstandings.

Note that JS also has (non-associative) arrays, with elements accessed via numeric indexes. These are also objects and so allow non-numeric key properties, but this is generally considered bad practice.

There are no associative-arrays in JavaScript. Everything is object.

Certainly they are similar but associative-arrays in JavaScript are just objects.