NATURALIZATION VERSUS CITIZENSHIP
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.