The terms "child selector" and "adjacent sibling selector" were old terminology used by the CSS2 spec when "selector" was a much looser term (it still is, but they use it more consistently now). It's related to "contextual selector" which is what CSS1 called selectors that used the descendant combinator. CSS2 introduced the term "combinator" to refer to the symbols themselves, but combinators themselves technically aren't selectors because they don't select anything on their own; instead, they indicate relationships between two (or more) selectors. MDN is not really correct in calling combinators selectors, but then again, it's all just semantics.
To answer your question, yes, "adjacent sibling selector" is an informal term. You can probably get away with using it even today, as it's easier to say by far than something like "a pair of compound selectors with the adjacent sibling combinator". Selectors 4 uses the much clearer and unambiguous name "next-sibling combinator" by the way.
To put it into examples:
+
is the adjacent sibling combinator (next-sibling combinator in Selectors 4), and
E + F
is an adjacent sibling selector (next-sibling selector) matching any F
that directly follows an E
.
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