Difference between blue and grey blue coaxial ports

There is no color code for telephone and video jacks. The one in your photo looks like a video jack for cable television.

The blue is just the connector. It looks like your house is wired for cable or dish. The dish network guy who wired my house a couple of years ago used a blue connector, a green, and two grays... They are all channeled to the same connection and the colors mean nothing unless there is some secret masonic code that I am missing. Your cat5e I am sure is in the light blue because it is a popular color for consumers and one of two colors (other is yellow) that is kept in stock at most stores in large strands.

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.

I couldn't help but read this and not let you all know what the difference is. I installed cable for years. White ports support a maximum of 1GHz signal pass-through, white blue ones support a maximum of 3GHz signal pass-through.

The color represents the frequency that that port will suport. Directv uses orange. Blue is a universal white is used by mostly Cox and local cable companies. There is also red

The blue and orange RG-6 barrel connectors in the wall plates are swept tested to 3GHz where some of the other (clear, white, etc.) that come with most wall plates you see on the walls are not tested above 750 MHz and will not be guaranteed to pass signals used by satellite providers, or MoCA devices.