In the textbook Topology by Munkers, Ascoli's theorem (45.4 and 47.1) refers to the fact that certain equicontinuous families of functions lies in a compact set, while Arzela's theorem is about certain equicontinuous sequences having a convergent subsequence.
In contrast, in the convention I'm familiar to, the term the Ascoli-Arzela theorem refers to a single theorem of the same vein. This convention is used in, e.g., the Wikipedia article about this matter.
Question: which kind of result does the term the Ascoli-Arzela theorem usually refer to? Is it about families of functions, or about sequences? Is the convention in Munkers's book where Ascoli's and Arzela's theorems refer to different things common?
(I'm mostly interested in the situations where the domain of the functions in question is more general than closed intervals in $\Bbb R$, which I believe what Ascoli and Arzela actually proved was about.)