Since there is no canon explanation, the one above could work well enough: grey is for the Ground Army, red is for the Space Navy, and the working environment of DS9 is exotic enough that both services are working side by side there. The attempt to take DS9 from Starfleet and the Space Militia federalists would be conducted by the Army exclusively, though.
Grey is good generic infantry camouflage (it worked for most of the WWII combatants), but red only works in certain rare outdoors settings and thus is more likely to be the color of an "indoors" military branch.
Certainly nothing indicates that the Bajoran uniform colors would denote department or occupation or skill set. If they denote branches of military, then it's only natural that two people of different color would have the same skill set and profession.
Timo Saloniemi