A person is alone when there are no other people around. A person is lonely when the presence of other people is missed. Neither implies the other; you can be lonely but not alone or alone but not lonely.
Can this distinction be made in Latin? If yes, is the contrast attested somewhere?
The words can be adverbs (alone), adjectives (lonely), nouns (loneliness), pronouns (solus), or anything else. The two words or expressions need not match the grammatical roles of the English counterparts, I just want to be able to make the semantic distinction. I know some words in the right direction (e.g. solus, solitudo) but I don't know whether or how to use them for this purpose.