I have seen this question http://wordpress.stackexchange.com/questions/131179/php-memory-limit-vs-wp-memory-limit and it has a really poor answer and the question isn't that good either. 

I am on a dedicated server and can do whatever I want.  I want to make sure our site runs as fast as possible and had `define( 'WP_MAX_MEMORY_LIMIT', '1024M' );` in our config.  

But then our theme had an update and I saw a screen that showed our PHP memory was 1024MB and our WP memory was 40MB.  I was like WHAT THE HELL.  So I added into the config `define('WP_MEMORY_LIMIT', '1024M');` and saw the WP memory had gone up to 1024MB.

So without beating around the bush can I get a very technical answer about what the difference in these two settings are.  Did me changing the WP memory limit really have any effect on my site?  If so are these setting named horribly?  (I fully understand how to allocate memory in PHP - looking at what limitations each setting put on my site.)