There is no difference that I can think of, except “I have no” sometimes sounds more formal and “I don’t have [any]” sounds more casual. Example: “I don’t have a car” sounds more casual and natural than “I have no car.”

"I have no" only applies for plurals. E.g. I have no books. You can't say 'I have no book.' "I don't have" can be both plural and singular. E.g. "I don't have a book." "I don't have any books" or "I don't have my card." "I don't have my cards." Hope this helped.

"I don't have (something)" means you simply don't have something. "I have no..." means you have none of something. "I have no..." would be equal to "I don't have any..."

Not is a function word (adverb) used to negate a word or a group of words. I have time to do it.........I do not (have any time to do it.). I have eaten my dinner........I have not (eaten my dinner). I love you because you are beautiful.......I love you, but not (because you are beautiful). 'No' can be an adjective meaning 'not any' or 'harldy any' or 'not a'. I have no time. I have no money. There is no answer to that question. She is no doctor.