Simple question, simple (brief) answer:
From the LabVIEW online help:
Queue: Use the Queue Operations functions to store data in a queue, which
you can later retrieve as individual elements or as an array of all the data
elements.
Notifier: Use the Notifier Operations functions to suspend the execution of
a block diagram until you receive data from another section of the block diagram
or from another VI running on the same computer.
So, basically the difference is in what you're trying to do. The notifier is used when you need to specifically wait until something happens before you continue. Also, one key difference is that a notifier does not buffer the data. This means that if you send a notifier and there's nobody waiting to "catch" it, and you then send another notifier, the first one is lost. In other words, the notifier is like a single-element queue.
What are you trying to do?