Not all browns are equal. Some are warm, close to cognac; others are cool, almost coffee. A light, warm belt with dark, cool shoes looks as if the two came from different wardrobes. The worst case is a colour that is almost the same: a black belt with very dark brown shoes, or two browns pulling in different directions. If you do mix shades, make the belt clearly lighter or clearly darker than the shoes, and keep the other accessories, a pocket square for instance, in the same tone as the belt.
With a suit the rule is stricter, because formality demands discipline. With a black suit, wear black shoes and a black belt. With navy or grey you can wear brown shoes, but then the belt should be brown too, preferably dark and smooth. Our guide on which shoes to wear with a navy suit covers the shoe side in detail.
Smart casual allows more freedom. Beige chinos, brown shoes and a belt one shade lighter usually look good, because the whole outfit is less rigid. Keep it logical: the more elegant the shoes, the more elegant the belt. With suede shoes, matte leather looks better than a high shine.
Finally, metal. A silver buckle with a watch that has gold details is not a disaster, but if you have the choice, stick to one metal: a silver buckle with a steel watch, gold with gold. It is not a strict rule, just a simple way to keep the details tidy.