You can become a citizen of the United States in a few different ways.  Sometimes it happens automatically by operation of law (as in the case of a child under the provisions of the Child Citizenship Act of 2000, or CCA: if the child is born to at least 1 US citizen parent who then gets a green card, then as soon as the child enters the US on that green card, the child becomes a citizen).  Sometimes it can be conferred. And of course, it can be obtained by filing for it.  In this case, the process is called naturalization.  That's what Form N-400 is.

The certificate you get when you file form N-400 is called a certificate of naturalization for this reason.  It is not the same thing as a certificate of citizenship, which is merely proof of citizenship that has already been obtained (say in the case of a child under the CCA).

If you lose your citizenship document - whether it's naturalization or not - you file Form N-565.  If you're applying to get a certificate of citizenship (i.e., that you already have) then you file Form N-600.