When you do a setcookie(), it adds the cookie to the HTTP headers that will be sent to the browser. It does not, in and of itself, store the data in $COOKIE or anywhere else. Once the user's browser has received the cookie (when the page is sent to it), any further page requests to that domain will send the cookie to the server along with the rest of the HTTP request. At that time any PHP script on that site will receive the cookie from the browser and add its name and value to the $COOKIE array.
Anyway, as far as login information goes, sessions are probably better, especially since you really don't want to be sending passwords back and forth to the browser via cookies, increasing the chance of them being intercepted, particularly in cases where other people might have access to the user's computer. (Note that sessions normally make use of a cookie, but it only exchanges a pseudo-random, generated session ID used to identify the session.)