Needn't

Needn't means
LACK OF NECESSITY
When used in the negative, must and have to have different meanings.
do not have to = lack of necessity.
must not = prohibition (DO NOT DO THIS!)
Lack of necessity may also be expressed by need not + the simple form of a verb. The use of needn't as an
auxiliary verb is chiefly British other than when it is used in certain common expression
In the other format, need behaves as a modal verb, like can, could, must should, etc. It has the same forms as modal auxiliary verbs: the third person singular has no s, questions and negatives are made without do. In this format, need is followed by an infinitive without to:

* You needn't bother to change the sheets. I'll sleep in them later.
* Need I lock the door when I leave? ~ No, you needn't. Sarah will be home soon.

In this sense, we are talking more about obligation and giving permission to someone not to do something. Note also that as a modal verb it is most commonly used in negative sentences and sometimes in questions.

In your examples, too, Christina, you are talking about obligation on the one hand, and necessity on the other. Compare the following alternatives to needn't and need to in the examples below:

* You needn't come if you don't want to.
Don't feel obliged to come if you don't want to.

* You don't need to be a genius to see that it is wrong.
You don't have to be a genius to see that it is wrong.