I could be wrong, but I think “puritanical conservative” is someone who has not bowed down to the liberal orthodoxy that controls the GOP. The say-anything and do-nothing liberal orthodoxy that wants conservatives to shut-up and just vote when called to do so.
Well, I’m a conservative, both fiscal and social. I find the republican party such slightly more to the right than the dems. I consider myself a conservative and not a republican. I wish there was a true conservative party that represented what I think.