What happens to a TCP session when the IP of a client changes?

I did a simple test of having netcat listen on a port, and connecting to that port from a client machine. I then changed the IP of the client while that nc session was open and sent some data, no data was received by server after changing the IP.

1. I know they are different layers, but does TCP use IPs for part of how it distinguishes sessions?
2. Does my example not work because of how the application handles it, or is this not working because of something happening at TCP/IP/Ethernet layers?
3. Does this depend on the OS implementation? ( I am most interested in Linux at the moment)