What Is the Difference between the “Longest Chain Rule” and the “Heaviest Chain Rule” in PoW?

The "longest chain rule" states that in case of a fork, nodes should always follow the chain with the most blocks. Bitcoin primarily uses this.

The "heaviest chain rule" is a refinement where nodes follow the chain that has the most accumulated Proof-of-Work (i.e. the most total hash power expended). For Bitcoin, these are usually the same, but the heaviest chain rule is a more accurate measure of security.