Gold coins are generally smaller than silver coins because gold is denser than silver. This means that a certain amount of gold, say one ounce, will take up less physical space than the same amount of silver.
To elaborate, the density of gold is approximately 19.3 grams per cubic centimeter, while the density of silver is about 10.5 grams per cubic centimeter.
This is why, when you compare a one-troy-ounce gold coin to a one-troy-ounce silver coin, the gold coin will often appear smaller in size even though they both contain the exact weight of precious metal.