SS application serves as your application to the academy. That is what my DS did, and when he received his email confirming that application it had his candidate number in it as I recall. So his application was in and processing before the nomination packets were due. But kinnem is correct, separate process. Says so right on the USNA applications page as well. https://www.usna.edu/Admissions/Apply/index.php#fndtn-panel3-Steps-for
And our senators / congressman had all different dates, and all different packages to fill out for their applications (similar, but each a little different). They were due between October and December as I recall. But earlier is better BTW, there is a lot of info and a lot of steps for you to keep track of along the way, no need to stress out by waiting and cramming. Good life lesson! Good luck!