When I view this page’s source in Internet Explorer, or download it directly from the server and view it in a text editor, the first space character in question is formatted like this in the actual HTML:
THIS character right here... " "
Notice the   entity. That is Unicode codepoint U+00A0 NO-BREAK SPACE. Chrome is just being nice and re-formatting it as when inspecting the HTML. But make no mistake, it is a real non-breaking space, not Unicode codepoint U+0020 SPACE like you are expecting. U+00A0 is visually displayed the same as U+0020, but they are semantically different characters.
The second space character in question is formatted like this in the actual HTML:
<p>Here's just with hitting the space key (which works fine)... <code>" "</code>.</p>
So it is Unicode codepoint U+0020 and not U+00A0. Viewing the raw hex data of this page confirms that:
