How would I distinguish ない as in the negative of ある and 無い the adjective? For example, if we have the sentence
食べ物がない
is the ない there just the negative form of ある or is it specifically the i-adjective? I always assumed the former, but recently while reading an older novel which used kanji for words that have mostly dropped them more recently, I did see 無い used in that way, and obviously the kanji made the distinction clear. I'd mainly find this concerning for polite speech, since there's a more obvious difference between ありません and ないです.
Thanks!