There are two distinct fruits which are called currants: (1) the dried zante grape; like a raisin, it is used in baked goods and (2) a fresh tiny berry related to the gooseberry.Currents are black, red, or white.here are two distinct fruits which are called currants: (1) the dried zante grape; like a raisin, it is used in baked goods and (2) a fresh tiny berry related to the gooseberry.