Limit theorems in probability theory show that asymptotically, the limiting distribution of a probabilistic system doesn't depend on the initial distributional specification. The most famous such result being the central limit theorem.
Many recent research works in Probability theory talk about universality, and sometimes they mention that limit theorem is an example of universality. But often results that they prove seem to be limit theorems.
So I seem to be missing if universality describes something more or is it a synonym for limit theorem?