At Mozilla, everything is called a bug. It's what other systems call an "issue". So it's too late for your terminology at Mozilla. (Example: I have a bug to improve the HTML output of my static analysis tool. There is nothing incorrect or flawed about the current output.)
replyAt Mozilla, but not everywhere: exploits are a subset of vulnerabilities are a subset of bugs.
Fwiw i think this is right. A bug is anything that doesn't do what you want it to do, and nobody should want a vulnerability in their software
replyWhen I worked at Mozilla, _everything_ was called a bug, whether it was a software issue, a problem in the office or some paperwork missing.
replyMuch as GitHub calls everything an "issue" and GitLab a "work item".