Is the "zen" in this usage related to the "zen" used with "zen Buddhism"

Nope. Whole nother word. You get that a lot in languages with lots of one syllable words. In Chinese, even with tones, you can get get several different readings of the same sound. That's why Chinese words are generally combinations of two characters. Built in redundancy clarifies meaning. In Japanese sometimes, if there's a chance of ambiguity in speech, speakers will draw the kanji on their palms to indicate which of several possible interpretations is the correct one.