fish_food
on its own (without parens) acts as a reference to the function object. It allows you to pass the reference to the function around to be invoked at some later date.
fish_food()
(with parens) is a function invocation expression, which causes the function to be executed. The function code is evaluated and run with a value optionally being returned.
With the AJAX code you supplied (and all async JavaScript involving callbacks) you want to use the fish_food
version (without parens). This passes the AJAX code a reference to your success function, to be executed asynchronously once the AJAX code has completed its round trip to the server and back.