<p>I am told that good developers can spot/utilize the difference between <code>Null</code> and <code>False</code> and <code>0</code> and all the other good "nothing" entities.<br>
What <em>is</em> the difference, specifically in PHP?  Does it have something to do with <code>===</code>?</p>

The differences between these values always come down to detailed language-specific rules. What you learn for PHP isn't necessarily true for Python, or Perl, or C, etc. While it is valuable to learn the rules for the language(s) you're working with, relying on them too much is asking for trouble. The trouble comes when the next programmer needs to maintain your code and you've used some construct that takes advantage of some little detail of Null vs. False (for example). Your code should look correct (and conversely,
wrong code should look wrong
).