is there a difference between white, red & black knights? if there is, can someone exp...

They represent the prince they are serving.

If I’m not wrong, White Knight are royal knight that usually accompany the King, usually seen when there’s a royal parade & such… They consist only nobles.
Black Knight are the one who mostly deal with the dirty work such as assassins, war, fighting monster.
And red knight are to work for people/civilians such as the security inside the cities/towns, investigation on any crime inside city, and when need to, they also will be required to assist Black Knight & White Knight.

thank you so much! it makes sense now (⌒▽⌒)

I thought black knights belong to the 2nd prince and red knights belong to the 4th prince and so on lol. This makes more sense.

So, the main knight are the white, black, and the red.
But each prince can scout some of those knights to form their own private guards or have their own small army, the knights can also apply for that. The other 3 princes have formed their own army because them 3 are fighting for the throne. The 4th prince was the weakest in term of politic advantage, and he is not that interested in fighting the throne with his brothers, so he doesn’t have any army of his own just yet.