The other answers so far are all quite good. Here's another way to think about it.
What's the semantic difference between a property and a field? I don't mean what are the technical differences, like a property is actually a pair of methods, blah blah blah. I mean, as far as understanding the meaning of a program goes, what is the difference?
A property is usually a public member of a class, and it represents a property of the thing being modelled. That is, you want to make a model of a newspaper so you make a class Newspaper and you give it a property Publisher. The publisher is a property of newspapers, so Publisher is a property of the Newspaper class.
A field is usually an implementation detail of a class. Maybe the Publisher property is actually implemented as a field. But newspapers do not have "fields", so you don't expose the publisher field as a public member of the Newspaper class; you use it as a private implementation detail of the Publisher property.
Events and delegates are somewhat analogous. An event is something in the model. A button is a thing that can inform you when it is clicked, so the Button class has a "Click" event. The delegate that actually does the informing is the implementation detail of the event.
