Termination and resign the same time?

I mostly want to know ----- if the day my manager tell me I  am terminated due to under-performance and let go, then I immediately submit my resignation letter. Does this count as quit or termination? I have only worked here for 4 months, really don't care about the package, I would like to be considered as resignation. If company wants to terminate with you, you have to sign some paper to indicate you accept this type of outcome, correct?