Can someone explain the laws governing paparazzi?

There are no specific laws governing paparazzi. They are subject to all the normal laws, just like the rest of us. For example, there's is nothing illegal about following somebody down the sidewalk. (In fact, private investigators do this all the time...only they try not to be seen.) Taking pictures of people in public places is not illegal either. You or I could take a picture of some strangers at a cafe anytime we want (of course, nobody would pay money for that).

But you can cross a line. Again, it doesn't matter if you are paparazzi or not...you cannot trespass on private property. Also, you cannot assault anybody. Blocking someone's progress on the street can be disorderly conduct. Similarly, you are right, you cannot stalk people or harass people. But, again, that is true whether you are paparazzi or not.

There are stalking laws in the US that often protect certain private information and/or protect people against threatening behavior directed toward them. It is possible that some paparazzi engage in conduct that could be considered stalking.

You can get a restraining order against one or two people, but not against the entire news industry.