They both run over UDP and always encrypt data. Beyond that superficial similarity they are completely different.

QUIC is a transport protocol that provides a stream abstraction (like TCP), with some improvements over TCP (like built-in support for multiplexing streams on the same connection, without head-of-line blocking issues).

Wireguard provides a network interface abstraction that acts as NIC. You can run TCP on top of a wireguard NIC (or QUIC for that matter).