Every research can be published once in journals and then be presented once on conferences. The situation you are stuck is different somehow. If you presented it on an international conference that doesn't publish the papers anywhere, as you said, you can take a deep breath. In contrast, if it happened inversely, submitting coincided with representing would not put you in trouble. Besides, as you said, this one is totally different from that one. Therefore, there is nothing to worry about. I think with informing them, you may pose a threat to your research.
GOOD LUCK
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