In the wiki page of Lattice-based Cryptography the "Worst-case hardness" is defined as below:
Worst-case hardness of lattice problems means that breaking the cryptographic construction (even with some small non-negligible probability) is provably at least as hard as solving several lattice problems (approximately, within polynomial factors) in the worst case. In other words, breaking the cryptographic construction implies an efficient algorithm for solving any instance of some underlying lattice problem.
But what is the difference between "worst case hardness" in lattice-based cryptography and "average case hardness" in standard cryptography based on discrete logarithm, say ElGamal Encryption?
It's seems to be confusing. For instance, breaking into ElGamal Encryption also leads to breaking several other cryptographic constructions and solving well-known number theoretic hard problem: computational Diffie-Hellman. However, that one does not considered a "worst case hardness".