It's more lightly amusing how things get framed.
As mentioned, puritan came in a few varieties back in the day. But yes, puritans as a whole tend to be painted with more of an extremist edge in school over here. While it isn't a huge point made, it is briefly covered that one of the key issues to puritans leaving the rolling green shores of England to head to the new world was in part because how stressed they were getting over all the religious tolerance laws that were being put in place. Not that they were universally tolerant laws, but more an attempt to tone down the various protestant/catholic squabbles and just happened to cover a few other areas.
But it's like anything taught. You get "one key element" and then they skim over a bunch of the other elements.