I've never encountered these expressions. They're clever, but I suspect they're redundant. Intelligent theists realize they can't literally prove their positions are correct, so they would all be "theistic agnostics" as you define the term. They would differ only in the degree of their personal doubts, but all would understand that proof is impossible.
In the non-theist camp, I'm aware of a few catagories of this position, some being weak versions of atheism, some strong. Each variety concludes that he doesn't believe because: (1) I don't know if gods exist; (2) no one can know if gods exist; and (3) I do know that gods do not exist. These are all different positions.