Ok I see what you mean about those squares and had seen them as well on some sites I visited. But it was when I upgraded my Win8.1 to Win 10 and installed a newer version of Opera that they became visible as emoji's that Opera/Win8.1 wouldn't display. I don't know if that is something helpful to you, but if you have done something different in between both those screen shots,it could be something to check out.
Also check to see if your Meta tag is for charset=UTF-8 or something else. I edit all my webpages with Microsoft's Word Pad manually, because in the past I've had "programs" change things that caused some things to not display as I wanted them to. I've never tried Front Page, maybe I'll also check out Expression Web.
I hope you figure it out, good luck!