I imagine the separation is mostly between the depth of mathematics background and research experience. It seems that, at least for Stanford, the GPAs are similar (listed on their site as 3.9 for Master's and 3.94 for PhD). Although the lack of a third digit on the former perhaps boasts what it is intended to obscure...
Couldn't tell from poking around a few department sites if there was a GRE Q difference between Master's and PhD students.
Thank you creed, and biostat_prof, for the feedback thus far.
I have another concern: Would Calc III or a Probability Class be more beneficia