The following evaluate to true:
new Number(2) == 2
new String(\"2\") == \"2\"
Obviously, but so do the following:
Because JavaScript has both primitive and object versions of numbers and strings (and booleans). new Number and new String create object versions, and when you use == with object references, you're comparing object references, not values.
new String(x) and String(x) are fundamentally different things (and that's true with Number as well). With the new operator, you're creating an object. Without the new operator, you're doing type coercion — e.g. String(2) gives you "2" and Number("2") gives you 2.