Two years ago, I applied to PhD programs (in Physics, if it matters); my undergrad was characterized mostly by underachievement, so my application was pretty weak (poor GPA, generic LORs, no research experience, etc.) Understandably, I did not get the response I was hoping for, and I decided to go for my Master's, both to put myself in a better position and to make sure academia is really what I wanted.
Fast forward two years and I'm in a bit of an awkward spot; I've done well in my Master's and I want to apply to PhD programs, but I'm not sure how to characterize my less-than-traditional path (it is relatively uncommon, at least stateside, to attend a terminal master's program in Physics). All aspects of my application are much better on paper (research, GPA, recommendations; except my GRE scores, which were already quite strong), but I'm worried about coming off as a second-rate student who couldn't make it the first time. Even my advisor, who thinks my application is otherwise quite strong, said he's unsure how it will be received.
Many of the schools I'm applying to are ones I applied to previously. Should I emphasize the upward trend through my Master's and how I've improved since my previous applications? Or is it not even worth mentioning (I could always use the extra space to talk about research) or possibly harmful?