The Network Layer (Layer 3) is responsible for transferring data from one device to another across multiple networks. It uses IP addresses to identify devices and relies on routing to choose the best path for data packets to travel. The Transport Layer (Layer 4), on the other hand, ensures reliable end-to-end communication between applications running on different devices. It breaks data into segments, controls data flow, checks for errors, and uses TCP for reliable communication and UDP for faster, connectionless communication.