The server listens on an address and port. For example, your server's IP address is 10.0.0.1, and it is listening on port 8000.
Your client IP address is 10.0.0.2, and the client "connects" to the server at 10.0.0.1 port 8000. In the TCP connect, you are giving the port of the server that you want to connect to. Your client will actually get its own port number, but you don't control this, and it will be different on each connection. The client chooses the server port that it wants to connect to and not the client port that it is connecting from.
For example, on the first connection, your client may get client-side port 12345. It is connecting from 10.0.0.2 port 12345 to the server 10.0.0.1 port 8000. Your server can see what port the client is connecting from by calling getpeername on its side of the connection.
When the client connects a second time, the port number is going to be different, say port 12377. The server can see this by calling getpeername on the second connection -- it will see a different port number on the client side. (getpeername also shows the client's IP address.)
Also, each time you call accept on the server, you are getting a new socket. You still have the original socket listening, and on each accept you get a new socket. Call getpeername on the accepted socket to see which client port the connection is coming from. If two clients connect to your server, you now have three sockets -- the original listening socket, and the sockets of each of the two clients.
You can have many clients connected to the same server port 8000 at the same time. And, many clients can be connected from the same client port (e.g. port 12345), only not from the same IP address. From the same client IP address, e.g. 10.0.0.2, each client connection to the server port 8000 will be from a unique client port, e.g. 12345, 12377, etc. You can tell the clients apart by their combination of IP address and port.
The same client can also have multiple connections to the server at the same time, e.g. one connection from client port 12345 and another from 12377 at the same time. By client I mean the originating IP address, and not a particular software object. You'll just see two active connections having the same client IP address.
Also, eventually over time, the combination of client-address and client-port can be reused. That is, eventually, you may see a new client come in from 10.0.0.2 port 12345, long after the first client at 10.0.0.2 port 12345 has disconnected.