Can someone point out the main differences between the two?
It seems that, at least conceptually, the two are very closely related. If I were to hazard a guess, I would say that the publish/subscribe method is a subset of the mediator pattern (since the mediator need not necessarily be used in the publish/subscribe manner, but the latter seems to require a sort of mediator object). Is that anywhere near close to it?
According to this page, the publish-subscribe model is an implementation of the mediator pattern.
Edit
I should note that the design patterns are called "patterns" precisely because there are going to be differences among every implementation. They aren't so much a set of decreed, canonical forms as they are a collection of observations on how people already write software. So there really isn't any way for a design to "strictly" adhere to a design pattern.
How I would describe the difference is that in mediator you probably care if the end application receives the message. So you use this to guarantee who is receiving the message. Whereas with pub/sub you just publish your message. If there are any subscribers they will get it but you don't care.