To my understanding by serverSocket = new ServerSocket(portNumber) we create an object which potentially can \"listen\" to the indicated port. By clientSo
Every TCP connection has as identifier the quadruple (src port, src address, dest port, dest address).
Whenever your server accepts a new client, a new Socket is created and it's indipendent from every other socket created so far. The identification of clients is not implictly handled somehow..
You don't have to think sockets as associated to "clients", they are associated with an ip and a port, but there is not direct correlation between these two.
If the same client tries to open another socket by creating a new one you'll have two unrelated sockets (because ports will be different for sure). This because the client cannot use the same port to open the new connection so the quadruple will be different, same client ip, same server ip, same server port but different client port.
EDIT for your questions:
By the way all these situations are clearly explained in TCP RFC here.