Difference Between php_admin_value[memory_limit] and php.ini memory_limit

There is no difference. There are different ways to set the same PHP configuration parameter. It's useful - for example - if you have a generic php.ini which gets loaded in all PHP-FPM pools, but in one of them you want to override a certain value - like memory_limit

See http://php.net/manual/en/configuration.changes.php

One difference between memory_limit = 256M in php.ini and php_admin_value[memory_limit] = 32M in pool.d/www.conf is that you can use ini_set('memory_limit','512M') to override the setting in php.ini but you can't override values set with php_admin_value.

Use php_value[memory_limit] = 32M if you want to allow it to be overridden. (php_value vs php_admin_value)