I can confirm that if I click "Reply" in a message I sent in a thread, the action taken is as if I was resending the message.  The TO address is the same person as the original TO address.

If I want to send (or reply) a message to myself, I need to add my e-mail address.  Yes, messages I send this way do appear in my Inbox as new.

If you have seen this change recently, is it possible that some change you made altered the action?

Items to check:
- Recent Browser Extension(s) added (disable them test, enable after)
- Any new "Labs" additions to Gmail? (Found in Gmail settings)
- Do other browsers act the same?