People hit this so much, it's maddening.
In this case, they're using Google Fonts, which already does the latter: https://fonts.googleapis.com/css?family=Poppins:400,600
Testing this on my own, I'm not seeing a difference between safari/chrome/firefox on macos. If there's only 400 and 600 weights present, they use the 600 for bold elements. If there's a 700, they use that. You only see faux bolding when there's nothing provided in the 600–900 range.
I think the difference here might be moreso about browser font handling on windows? Though I'm still not sure how they got to the bold result at the top of the screenshot…I wouldn't expect safari to apply a faux bold when the 600 weight is there, and that sure looks like the proper 700 which apparently wasn't being called.
Sidenote: I didn't know about the font-synthesis property until this. Looks like it is intended to prevent any sort of faux bolding or faux italicizing from happening. That's cool.