DHCPv4 uses the MAC address and an optional client ID to identify the client for purposes of assigning an address. Each time the same client arrives on the network, it gets the same address, if possible.
DHCPv6 uses basically the same scheme but makes the client ID mandatory and imposes structure on it. The client ID in DHCPv6 consists of two parts: a DHCP Unique Identifier (DUID) and an Identity Association Identifier (IAID) . The DUID identifies the client system (rather than just an interface, as in DHCPv4), and the IAID identifies the interface on that system.
DUID+IAID can also be used with DHCPv4. These can be concatenated together unambiguously so that they can serve as the client ID. For compatibility reasons, this is not done for regular IPv4 interfaces. However, for logical interfaces (net0:1), DUID+IAID is used if no client ID is configured.