Actually ZR5K is very different from C25K.
ZR5K incorporates a short set of leg exercises with run/walk drills, followed by an extended "free-form run" in the end in which the instructor tells you to run, but allows you to slow to a walk as necessary. By week 4, however, the instructer encourages you to "push yourself a little this time" while still saying to slow down if you need to. As the weeks pass, the free-form runs get a little bit longer.
C25K is strictly Run/Walk drills, with the Run segments getting longer each week. It's easy to see why people feel the need to rerun some weeks because it creates some sort of pass/fail mentality if they can't run during the run segments.
I've put together a pdf of the ZR5K workouts if anyone wishes to use it without having to use the app. But just know the app is more than half the experience. I definitely recommend buying it if you were going to do this workout.
Download
And for comparison, here's the link to the
C25K workout schedule.