I'm not even sure what is the same and what is different, and there isn't anywhere that I found that explains it easily (if it can even be explained easily).

I think the difference might just be in the rendering engine. So Safari uses "safari", and WkWebView uses straight WebKit? But even that isn't true since there are things that WkWebViews support that WebKit doesn't...

But there are many differences between them. The WebRTC stuff above as one, but also things like appcache manifest stuff didn't work in WkWebView in iOS 9 (even though it worked in Safari). And that violation was especially egregious because it could be enabled by calling a single private Objective-C method like this

     [_wkWebView.configuration.preferences _setOfflineApplicationCacheIsEnabled:YES];

However apple would then deny your app in the app store if you did that...

So I genuinely don't know what to think.

Oh, and SFSafariViewController won't even save you, as that doesn't support WebRTC either...