Are the expressions: "You needn't" and "You don't need to" different in meaning? [duplicate]

Solution 1:

As a teacher of English as a Foreign Language, my take on it is that the differences are too small to be of interest to anyone except linguists, poets, and authors.

There is, however, one difference that you accidentally highlighted. Notice the stress you placed on need in your second example sentence:

"You don't need to listen to him."

You could have just as easily placed the stress on don't, or not stressed any of the words. You have fewer choices of sentence stress in the you needn't form, and this probably affects the nuance in ways I'm not really qualified to discuss.

Why or when did "need" become a modal verb?

There is a large grey area between the modal auxiliaries and the ordinary verbs. The trend seems to be that, in forms like:

subject verb1 verb2

verb1 tends to get reanalysed as a modal auxiliary. For instance, will used to be a plain verb, meaning want to (and want used to mean lack).

Solution 2:

There is no difference in meaning. But you needn't speak like that if you live in the States or they may mistake you for a Brit.

My apologies. Let me clarify what I was meaning in the sentence above. It is really a matter of dialect. It is not nearly as common in the States to hear "you needn't" as it would be in England (and therefore one may mistake you for a 'Brit'). I upped your comment for making me aware of my cause of confusion & hoped it would alert you that I attempted to answer your question (sorry I'm new and don't know how to chat).