Banks are a part of a wire transfer network called FedWire. All of these transactions are routed from bank to bank through a central computer at the Federal Reserve Bank, kind of like a wide area network (WAN). Banks which are not big enough to have their own Fed account use the services of a larger bank (correspondent relationship). The transfer of money between large banks, where the routing is bank->Fed->bank, is almost instantaneous. More time may be required for correspondent banks because the route is less direct - correspondent->large bank->Fed->large bank->correspondent. Each stop along the way will have their own procedures and timeframes (within regulatory minimums) for forwarding the transaction.
I don’t know for sure, but I assume WU transfers go through what is basically a corporate WAN. In that case you can only transfer between WU offices (not from WU to a bank, for instance).
I have no idea what system Paypal uses but you inadvertently answered your own question. In order to offer the service for free, they sit on your money for 2-3 days and keep the interest. It’s called float. If you make a $100 purchase and Paypal can generate 5% interest for 3 days they make about .04 on your transaction. Process a million tranactions per day and you start talking about real money.