The first is the dried fruit that is basically a raisin; it’s made from grapes (see Zante Currants.)
The second is the fresh red, white and black Currants that are in fact berries.
The following applies to the dried fruit type of currants:
1 cup = 6 oz = 175g
2 3/4 cups = 1 pound = 450g
3 tablespoons = 1 oz = 30g
Currants (the raisin kind) traditionally came from Corinth, Greece which shipped small raisins (dried grapes) throughout Europe.
The word “currant” is a corruption of “Corinth”.
Since the berries are about the same size as the raisins, the name currant was applied to them as well starting around the mid 1500s.