I'm not sure why the tiny, jewel-like fruits known as currants have the same name as the small, dried, seedless grapes - they have very little in common.
Fresh currants grow on long strands and the most common variety is red currants. Black is seen less often and white currants are rare. Red and black currants have a tart, astringent flavour and are best when cooked, while white currants are sweeter. Black currants are made into sweet syrups (such as Ribena) and the liqueur creme de cassis.
When buying currants, the berries should be plump and shiny. Check carefully for mould.
In Hong Kong, I've only seen red currants and they're sold in small punnets. They have a high pectin content and are used to make preserves, but I've never used them on their own because they are so expensive.
Instead, I cook currants with strawberries and blueberries (which are both low in pectin) to make three-berry jam. I also put them in financiers - small, buttery almond cakes baked in rectangular moulds so they resemble gold bars. After mixing the batter and putting them in oiled moulds, gently press in a few currants. Bake as usual then serve warm.