Welcome to English Forums! The definition you quote seems to be using the terminology of transformational grammar, because it uses the term "constituent". This is in contrast to the terminology of so-called "traditional grammar" in many cases.
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AnonymousAdverbial refers to a function which adverb (a word class) can have in a sentence. Sentence adverb and adverbial are two different names for the same functional constituent.Sorry, I don't understand your definition. Would you please elaborate.
Can you see why I have trouble with the definition of these terms?Yes! It is a troublesome topic!