TCP connection termination can be achieved through two methods: three-way handshake and four-way handshake. In the three-way handshake, the client sends a FIN segment to indicate it wants to close its side of communication (half-close). The server responds with an acknowledgment and its own FIN segment, signaling closure from both sides after receiving a final acknowledgment from the client. In contrast, during a four-way handshake, if the server still has data or operations pending when it receives the client's initial FIN signal, it first acknowledges receipt but completes those tasks before sending its own FIN segment for full termination.