Well, there's about a dozen things wrong with this circuit...
But generally, when you see a C, R+C or other timing network around an op-amp, it's being used as an error amplifier. Not a comparator.
The distinction is very particular.
At DC, there is no difference: except for an error amplifier of limited DC gain (no integral term), the output of an error amp will be saturated, just as a comparator's will.
At high frequency, the difference is significant.
A comparator is intended to produce its comparison as quickly as possible, on the order of nanoseconds. It's supposed to look comparator-ey from DC to quite high AC frequencies.
Op-amps (specifically, of the dominant pole compensated type, but that's not important just yet), and error amps in general, are designed to produce a slow, gradual response to an input. The gain goes from very high near DC, down to unity (1) at some cutoff frequency, give or take some desired characteristic. They are designed for use in a feedback loop, so that changes in the load can be adjusted for in real time. The frequency characteristic is necessary to account for delay and lag in the load: obviously, one cannot achieve a stable control (meaning, the change over time eventually goes to zero and it stabilizes) if the load is always being switched suddenly on and off due to every tiny little fluctuation!
Applying some math, one can determine just how slow and gradual the error amp must be, for a known load.
Tim