Yes. And no. I explain. If you are going for a classic look or want to follow the fashion rule on this, then yes they should match. However if you want to break the rule or is betting on a more casual look or even if you have a more alternative look, then they don’t. Let me illustrate it better.
With a suit, usually it is a good idea to match shoes and belts not only in the color (and preferable even in the shade of it) but also in the vibe (dress up or down vibe). If you want to go absolutely classic on that. If you want give a little edge to it, then you cam mismatch the shade of color, betting in a dark brown shoes and a medium brown belt. Or in a opaque black shoes and shiny black belt.
And yes, even with a suit there is a possibility of going beltless. Even if your pants have the place to wear a belt. Even without suspenders. It is up to you.
To be honest, I don’t like the idea of wearing, let’s say a brown belt to a black shoes. And vice-versa. Mostly. The only exception for me is in the case that your pants are black and you are wearing brown shoes. The vice-versa here sometimes don’t work as well.
And if by any chance your fashionable self are betting in a gray shoes then your belt could be gray, brown or black.
In a more casual look, then you don’t have to match shoes and belts. Although the deal with brown and black is the one to approach with caution here. Not always is gonna be a good idea.
And speaking of brown… this is a great bet to pair with colored shoes like sneakers, driving shoes, espadrilles etc. Beige is also a good bet. Black? Not so much. But it is possible.
And yes, it is a good idea to bet on belt that is more casual. I will talk more about it in another post.
And although I did this post with men in mind, women can also take a clue from it.