1 client, 2 servers
I made a client-server program set, that's server will receive the message client sent.
If the server program is in multiple different computers on the same local network, and client opens a connection to the server program, do all server programs in the local network receive the connection and the message?
The client must specify the end-point of the connection. With any stream-oriented protocol like TCP, this cannot (I think) even be a broadcast. The client must connect to a specific port of a specific IP. There can only be one program ever be listening to the same IP and port.
Thus, the client will only connect to one server, unless you create more than one connection.
tcp is one-to-one, or direct connection. servers may share data. this process is independent of tcp.
You might want to look into sending a UDP pack to the broadcast IP which will be recieved by all IPs.