A polyfill is a shim which replaces the original call with the call to a shim.
For example, say you want to use the navigator.mediaDevices object, but not all browsers support this. You could imagine a library that provided a shim which you might use like this:
<script src="js/MediaShim.js"></script>
<script>
MediaShim.mediaDevices.getUserMedia(...);
</script>
In this case, you are explicitly calling a shim instead of using the original object or method. The polyfill, on the other hand, replaces the objects and methods on the original objects.
For example:
<script src="js/adapter.js"></script>
<script>
navigator.mediaDevices.getUserMedia(...);
</script>
In your code, it looks as though you are using the standard navigator.mediaDevices object. But really, the polyfill (adapter.js in the example) has replaced this object with its own one.
The one it has replaced it with is a shim. This will detect if the feature is natively supported and use it if it is, or it will work around it using other APIs if it is not.
So a polyfill is a sort of "transparent" shim. And this is what Remy Sharp (who coined the term) meant when saying "if you removed the polyfill script, your code would continue to work, without any changes required in spite of the polyfill being removed".