The Nazi Party was a political party in Germany, founded in 1919 by Anton Drexler. At first it was called "The German Worker's Party".
When Hitler later took over the party, helped by his oratorical skills, he renamed the party the NSDAP (Nationalsozialistische Deutsche Arbeitpartei), meaning National Socialist Germany Workers' Party.
Later on the Great Depression helped the Nazi come to power in 1933.
Paul von Hindenburg, the president at the time, appointed Hitler Chancellor of Germany on January 30th 1933. Within 3 months, he had assumed dictatorial powers.
Hence, the Nazi Party is indeed what Hitler used, and what helped him to gain power and wage war across the globe.
Bob : "Well, looks like the Nazi Party did help Hitler get into power"
John : "Yea but it was full of homos, go read "The Pink Swastika"