I don't think this is a question for this sub because it's a simple question of terminology. While both terms get thrown around rather loosely, a Nazi in its original meaning was a National Socialist or a member of the NSDAP (the German Nazi party), while a Neonazi is someone that is in some way affiliated with that movement (mostly in name and ideology) but is doing so well after the demise of the Nazi party.

Typo, title should say differentiate.

Everything is extremely simple. Nazism is the ideology itself, the Nazi Party itself (let's say the same Germany). Neo-Nazism is an attempt to imitate the original Nazism. The Nazis are, in fact, no one can be counted. No one is directly in the Nazi parties, the same ideas are no longer promoted directly. And neo-Nazis are just trying to imitate the Nazis of those times.

The term Nazi is used to describe either anyone who subscribed to Nazism as a political ideology and/or was a member of a political party that espoused Nazism from about 1918 to the end of WWII. A neo-Nazi is anyone who subscribes to Nazism as a political ideology and/or was/is a member of a political party that espouses Nazism post-WWII.