What's the difference between these?

I have no means you do not posses something, while I haven’t got can mean I haven’t received the thing or just I do not have, which simply means I have none of that thing. Examples: I have no oranges. I haven’t got any oranges in my house. I haven’t got the oranges you promise me.

A very common way to express this is “I don’t have a… /I don’t have any…”

It depends on the context. Sometimes they mean the same things. Sometimes different. Sometimes, only one makes sense. It can depend on accent, dialect, tone, and many more subtle things. There are thousands of ways to use them. "I haven't got sugar" and "I have no sugar" probably means the same thing. But sometimes, the last means you don't *want* sugar in your tea. "I haven't got bananas" is (usually) the same as I have no bananas. Except the last one is a well-known song, so it's a sort of "meme" to some people. "I haven't got the strength" suggests you are too weak to perform a task, where "I have no strength" means you're totally exhausted. "I haven't got fatter" is OK; "I have no fat" is bizarre. "I haven't got children" is quite factual, "I have no children" may sound sad. Sometimes, "any" is required. "I haven't got any idea" is similar to "I have no idea", but the latter is a more common phrase. "I haven't got money" is slightly strange and ambiguous. It could mean that you don't have *enough* money. "I have no money" makes it clear you have none at all. "I haven't got *any* money" is (almost) the same. "I haven't got married" is OK. "I have no marriage" or "I have no wife" is very different.

I haven't got a clue. Also, I have no clue. Sorry.