I've read the FAQ but still not sure.
Criteria for certain mechanics, like a question ban, involve "badly received" posts, one of which is "closed questions". Also "Curious" badge requires "a positive question record", which takes this into account.
As the FAQ says, reasons like off-topic, too broad, unclear what you're asking are given for closing a question. So does the closing banner, which says "put on hold/closed by [user] for [reason]". But duplicate questions are given "marked as duplicate by ...".