Address is a full unique identifier. Connectionless delivery needs address on every packet.
Connection-oriented delivery may use a short hand that shows the connection rather than the destination.
As an example let's take an ATM with 16-bit address, 24-bit connection identifier and connection identifier adds.
-8-bit Virtual Path Identifier (VPI)
-16-bit Virtual Circuit Identifier (VCI)
The connection identifier is local to every computer and it can be different at different segments of the ATM switch.