Sometimes, the same word or phrase can be interpreted either as a disjunct or as a simple adjunct:
More generally, the term disjunct can be used to refer to any sentence element that is not fully integrated into the clausal structure of the sentence. Such elements usually appear peripherally (at the beginning or end of the sentence) and are set off from the rest of the sentence by a comma (in writing) and a pause (in speech).
A specific type of disjunct is the sentence adverb (or sentence adverbial), which modifies a sentence, or a clause within a sentence, to convey the mood, attitude or sentiments of the speaker, rather than an adverb modifying a verb, an adjective or another adverb within a sentence.
An example of a sentence adverb modifying a sentence is: Unfortunately, when I got to the supermarket it had run out of the vegetable I like. An example of a sentence adverb modifying a clause within a sentence is: I liked the red car in the forecourt, but unfortunately, when I got to the dealer it was already sold.
"Unfortunately" thus communicates the regret or disappointment the speaker experiences and so manifests as a sentence adverb the sentiments of the speaker.
"Unfortunately," however, is only one of many sentence adverbs that can modify a speaker's attitude. Others include "mercifully," "gratefully," "oddly," "admittedly," etc.
One of the reasons the sentence adverb usage seems more acceptable these days is that its semantics are reminiscent of the German hoffentlich ("it is to be hoped that") which implies (in the context of the first example) that the speaker hopes the sun will shine. Furthermore, it is because of their conciseness, avoiding the need to put into several words what can be said in one, that the use of sentence adverbs is establishing itself more and more in colloquial speech.
Merriam-Webster gives a usage note on its entry for "hopefully" in which the editors point out that the disjunct sense of the word dates to the early 18th century and had been in fairly widespread use since at least the 1930s. Objection to this sense of the word, they state, only became widespread in the 1960s. The editors maintain that this usage is "entirely standard.