Martin -- the word поп does indeed mean "priest", but it's considered very old-fashioned nowadays and can even have a dismissive sound. But it would be an appropriate word if you were quoting Henry II in regard to Thomas a Becket ("Will no one rid me of this meddlesome поп?"). And I guess that the husbands of the women that Fyodor sleeps with might also use the word!

And священник "by default" refers to Orthodox or Catholic priests, but in some contexts it can also be used generically for Protestant ministers, Jewish rabbis, Muslim imams, etc., -- so in such cases it would be translatable as "clergyman" or "man of the cloth".