Multiplexer takes several inputs and gives a single output, while demultiplexer takes a single input and gives several outputs. They both follow combinational logic and work on different operational principles - multiplexer is many-to-one, while demultiplexer is one-to-many. Multiplexing and demultiplexing at the transport layer allow data from multiple applications to be transmitted simultaneously over a network from source to destination, where it is directed to the appropriate application.