Frum for marriage: You’re married and you don’t believe in Judaism, but for some reason you still want your kids to go to yeshiva. I have met families in which both the husband and spouse weren’t believers or frum, but they wanted to keep their kids in the yeshiva system and they themselves wanted to remain within the community for some reason so they hid this fact from their friends and children.
Frum Atheist: You can do it all and not believe in God, I totally understand so how someone can separate the stuff. I mean, most of Judaism makes no sense even if you believe in God, but for many folks it’s a way of keeping the culture alive – kind of like secular Jews who eat pork on Yom Kippur yet would have an aneurysm if their child married a goy.
Orthoprax: closeted off the derech, someone who is orthodox in look, community and act, but doesn’t believe in it, I would venture to call them Frum Non-believers, but not necessarily atheists, because you can have a full belief in God even if you aren’t into the daily leather strap ceremonies.