I wouldn't substitute 'thread' for 'issue' in conversation. I come from the Midwestern USA. To me, an 'issue' is the underlying problem under discussion.
I might, however, say something like, "I've lost the thread of this discussion" meaning, "I'm confused. What were we originally talking about?"
My 'taxonomy' of the words you listed would be: Topic, Subject, Issue, Thread. I can imagine a TV debate moderator saying, "Tonight, our topic is Politics. Our subject is Immigration. The issue is: Should asylum seekers be allowed easier entry into the United States?"
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