Wiktionary
uniform continuity
n. (context analysis of a function English) The property of being uniformly continuous.
Wikipedia
Uniform continuity
Every uniformly continuous function between metric spaces is continuous. Uniform continuity, unlike continuity, relies on the ability to compare the sizes of neighbourhoods of distinct points of a given space. In an arbitrary topological space, comparing the sizes of neighborhoods may not be possible. Instead, uniform continuity can be defined on a metric space where such comparisons are possible, or more generally on a uniform space.
We have the following chain of inclusions for functions over a compact subset of the real line
Continuously differentiable ⊆ Lipschitz continuous ⊆ α- Hölder continuous ⊆ uniformly continuous ⊆ continuous