What exactly is the difference between supervised and unsupervised learning?
The difference is that in supervised learning the "categories", "classes" or "labels" are known. In unsupervised learning, they are not, and the learning process attempts to find appropriate "categories". In both kinds of learning all parameters are considered to determine which are most appropriate to perform the classification.

Whether you chose supervised or unsupervised should be based on whether or not you know what the "categories" of your data are. If you know, use supervised learning. If you do not know, then use unsupervised.

As you have a large number of parameters and you do not know which ones are relevant, you could use something like principle component analysis to help determine the relevant ones.