Difference between blue and grey blue coaxial ports
There's no difference between the colors. In locations with lots of different AV sources, different colored connectors are used to differentiate between sources. I'm guessing one installer had a pouch full of blue connectors, and another installer had gray.   

The connectors in your home may have come from different manufacturers, or different times in history. So there may indeed be a difference in quality, and/or construction.  This, however, has nothing to do with the color of the connector. 

F connectors (and coaxial cable) are commonly used to transmit cable, satellite, and broadcast television signals.