TLDR; In addition to the accepted answer; One is implicit and one is explicit.
When the HTML you've written or had generated by an application/library/framework is read by your browser it will do it's best to interpret what your HTML meant (which can vary from browser to browser). When you use the HTML entity codes, you are being more specific to the browser. You are explicitly telling it you wish to display a character to the user (and not that you are just spacing your HTML for easier readability for the developer for instance).
To be more concrete, if the output HTML were:
<html>
<title>hello</title>
<body>
<p>
Tell me and I will forget. Teach me and I
may remember. Involve me and I will learn.
</p>
</body>
</html>
The browser would only render one space between all of these words (even the ones that have been indented for better developer readability.
If, however, you put the same thing and only changed the <p> tag to:
<p>Hello There</p>
Then it would render the spaces, as you've instructed it more explicitly. There is some history of using these spaces for styling. This use has somewhat been diminished as CSS has matured. However, there are still valid uses for many of the HTML character entities: avoiding unexpectedly/unintentionally interpretation (e.g. if you wanted to display code). The w3 has a great page to show the other character codes.