Vs. Modal adverb: 'Will there be any food left over?' he asked hopefully.
Distinction
Adverb
Express the quality of the action or property
Adverbial modifier
Modal word
Express the speaker’s view concerning the reality of the action
Parenthesis as a part of the sentence
Semantic classification
Expressing doubt (perhaps, maybe, possibly)
Expressing certainty (certainly, surely..)
… (lexical matter)
Syntactic classification
Interjection
Latin inter ("between") and iacere ("throw").
Words expressing feelings, curses, and wishes, or are used to initiate conversation
Ouch! damn! Hi!
Often have onomatopoetic characteristics: Brrrr! Whoops! Pow!
sometimes called "filled pauses“:
uh, er, um
Outdated Dispute:
A word or an involuntary outcry?
Not names but expressions of emotions
Limited possibility to be part of a phrase: oh dear!
Sometimes, however, interjections combine with other words to form sentences, but not with finite verbs: Good gracious! Well I never!
D.Crystal: as the punctuation marks indicate, they are better treated as a type of sentence rather than as a word class.
Outside the sentence structure or
A part of the sentence (parenthesis)
No element belonging to a sentence can be outside its structure.
Sentence-words because they can replace or be replaced by a whole sentence.
Pro-sentence
A pro-sentence is a function word or expression that substitutes for a whole sentence whose content is recoverable from the context.
Pro-sentences are a kind of pro-forms and are therefore anaphoric.
In English, yes, no, and okay are common pro-sentences.
In response to the question "Does Mars have two moons?", the sentence "Yes" can be understood to abbreviate "Mars has two moons."
Pro-sentences =grammatical interjections, since they are capable of very limited syntactical relations.
vs.
a distinct part of speech, given that (other) interjections have meanings of their own and are often described as expressions of feelings or emotions.
Conventions like Hello, Bye, and Goodbye are interjections, as are exclamations like Cheers! and Hurray!
Well can also be used as an interjection, for example when put at the beginning of a sentence. (Well, what’s up?)
"Excuse me!", "Sorry!", and similar ones often serve as interjections
Structural classification
Words
phrases
sentences
Oops!
Oh dude!
As I entered the room — Oh, my gosh! What I saw! — he was still standing there.
Open-class words, i.e. new words may be added readily.
Literature
Иванова И.П., Бурлакова В.В., Почепцов Г.Г. Теоретическая грамматика современного АЯ. – М., 1981.
Ильиш Б.А. Строй современного английского языка. – Л., 1971.
Теоретическая грамматика английского языка / Отв. ред. В.В.Бурлакова. – Л.: Изд-во Ленингр. Ун-та, 1983.
Bussman H. Routledge Dictionary of Language and Linguistics. 1996.
CGE = Carter R., McCarthy M. Cambridge Grammar of English. – CUP, 2006
Crystal D. The Cambridge Encyclopedia of the English Language. – CUP, 1995
Peters Pam. The Cambridge guide to English usage. – CUP, 2004.