Same theology, different terminology.

I'd beg to differ. If Jesus has one nature which is both divine and human, wouldn't that mean he is not both fully God and fully man, which would be necessary for our salvation?

No, it wouldn't mean that.

“the unassumed is the unhealed.” -Gregory Nazianzen. This means that whatever Jesus did not assume he didn't heal with His sacrifice, meaning if He did not take on a truly human nature he could not heal from human nature. "and by him everyone who believes is freed from everything from which you could not be freed by the law of Moses." -Acts 13:39, ESV. (Gregory Naianzen was an early church father during the 4th Century AD.)

I don't believe that the Coptic formulation denies that in time, Jesus did truly assume humanity. (If that were the case, I would have to retract the meme and issue an apology and clarification.) And I would certainly agree here with Saint Gregory, but as I understand it, the Coptic church uses the word "nature" to describe the being of Christ, while the standard formulation uses that word to describe two aspects of Christ. ("Aspect" isn't my favorite word to use there, but I think it gets the point across.)