They are separate however I did take the PFT and MEPS the same day, it all depends on location, what you recruiter has planned, and how fast you get through MEPS. Just talk to your OR. When I went I didn't even say anything and they kept putting me in front of line since I was BDCP so I had plenty of time for the ASTB and PRT. Three ducks with one stone.
I would not have stood a chance if I took the PRT on the same day as MEPS. I ended up being one of the last out, and my morning Pop-Tarts (baaad idea) had to last me from 0500 until 1500 or something like that. I never could have run after that.