They are not exactly the same. As was said, the first implies that you have been waiting, and you are wondering how much more you have to wait. The second is asking for the total wait time. It could be asked at at any time...even after you have been waiting. Do show it with math: wait time is 30 minutes "How long do we have to wait?" : 30 minutes we have been waiting for 10 minutes already... "How much longer do we have to wait?": 20 minutes more (10+20 makes 30)

1 implies you have already been waiting for a long time. 2 could be said as soon as (or before) you start waiting.

within the meaning of absolutely the same.