Depends on the composition, you get metal loaded ones, which are either silver or copper, but the majority are white zinc oxide powder finely ground with a silicone oil grease as the binder and transfer agent. The silicone does evaporate out with time and heat, so does need periodic refreshing. The metal loaded are somewhat conductive, but the white is generally not, but still is in need of the insulator to provide the actual insulation, as it can break down with a thin film and voltage applied to the thin film.
I have made my own before, using zinc oxide powder and some pink Dow corning silicone grease, because I was using 5 or 6 tubes per job changing UPS transistors. For a few recent ones I refreshed the existing compound using a tiny amount of Beyer silicone oil, as I have a bottle I use to apply to phone screen protectors, to get rid of edge bubbles. 100ml is a lifetime supply of that, and as it is so thick it acts well for thermal transfer. For a CPU interface with a lid there is no difference between the cheap common white, and any of the fancy ones, the biggest loss is the internal transfer compound in the CPU.