You are dead wrong on both points.
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Conservatives are simply those who espouse conservative positions. Tankies espouse conservative positions. They are the literal definition of conservatives.
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Nazis frequently call themselves nazis. In 1940's Germany, you could be sent to a concentration camp for not identifying as a nazi. They used the word specifically. (Although in the 30's, nazis often just referred to themselves as "conservatives".) In the U.S., an official "Nazi Party" preceded WWII. A different American Nazi Party exists today and members still refer to themselvss explicitly as nazis. Proudly. In fact, there are currently several organizations whose members call themselves nazis or neo-nazis.
Conservatives are pathological liars. I do not respect my enemy, nor those who defend my enemy. So, without respect, "I don't think you know what you're talking about and should therefore butt out."