Usually FH - any color, but 80% - attack, even spikes. BH - any color, but either smooth or spikes or more for protection. It all depends on how you play. And from the type of foundation.
Various pads can be glued to the sides of the racket, which can give the ball spin or extinguish it due to their characteristics. And a different color of the pads is needed so that the player can understand what the rotation will be after the opponent hits the ball with one or another side of the racket.
To begin with, in professional table tennis, each rubber is bought and glued separately. You can buy 2 completely identical overlays or 2 different ones. Well, in general, yes, having one red and another black requires a rule.
There are many types of rubbers: attacking and defensive, with strong rotation, spin damping, spike and so on. And it often happens that one side is put on one cover (say, attacking), and on the other - another (for example, protective spikes). The opponent may ask you to show your racket before the game so that you know what to expect.
And so that the opponent can see what kind of coating you hit, rubbers and made in different colors. This is a kind of good manners, respect for the opponent.
If they are both the same to the touch, then none. Sometimes the black side has a texture, which is used for a "defensive" style of play. It kind of helps to stop the ball from spinning or something. Correct if I'm wrong)