The Govt doesn’t have jurisdiction over the entire web, which is one big enforcement problem that makes Justice look very carefully at the situation before getting involved. In some cases US can get jurisdiction based on treaties between us and other countries, where we each help each other police the web, or based on the fact that an entity of the US is doing business in some foreign country. but it’s not an easy task and therefore is usually limited to situations where there’s a big harm being done (e.g. hacker is committing espionage or is ripping off Bank of American for a billion dollars and putting the money in a swiss bank acct). furthermore the US Govt/DOJ etc. really doesn’t WANT to control the web—policing it would be a losing battle and it would hamper economic growth too much.
If you are talking about whether the courts can get jurisdiction in a lawsuit between two private parties, e.g. RIAA sues Kazaa, that’s a whole different kettle of fish jurisdictionally speaking. But that is a different question than whether the US govt has or wants to get involved. and that is basically the difference between civil and criminal legal actions. the US Govt has to be very selective as to what it chooses to criminally prosecute, because it has lots of crimes and limited resources. but private parties can sue each other on any non-frivolous grounds as long as they have the time and money to hire lawyers and go to it.
as for your question about whether Morpheus and Kazaa are "different", I think what you are referring to is a network that’s peer-to-peer with nothing passing through a central server. If nothing is passing through a central server, or there is no central server, it’s legally hard to go after the entity Morpheus or Kazaa (grounds are lacking under the current law, although this could be argued back and forth). and therefore RIAA would have to sue or penalize end users which is a pain in the butt since there are lots of small users and it would be costly to go after each one in a private lawsuit and probably impossible to catch everybody. as it would also be impossible for the govt to go after each small user and fine or prosecute them.