I believe cordial is a term used most commonly in the UK. You may also know it as squash. It's not traditionally an alcoholic drink as it is essentially a concentrated fruit syrup, which is diluted with water to make a refreshing drink.
Of course, you can mix it with alcohol. and it's a great mixer or cocktail ingredient, but it's not technically alcoholic in it's preparation and it's most commonly used as a soft drink. It's a great way to jazz up some plain water.