Hard sauce; it's all to do with alcohol.

In North America, the term hard liquor is often used to distinguish distilled alcoholic drinks from non-distilled ones, whereas the term spirits is used in the UK.

So brandy butter is known as hard sauce in North America. Rum butter is an alternative, certainly in England.

And apple juice is often called cider in North America, where fermented apple juice is called hard cider. In the UK, cider refers to fermented apple juice, called cidre in France. While sweet apple juice comes from dessert apples, traditional cider is made from bittersharp and bittersweet cider apples.

Soft drinks are the alternative to hard drinks. 'The term soft drink was originated to distinguish the flavoured drinks from hard liquor, or distilled spirits. Soft drinks were recommended as a substitute in the effort to change the hard-drinking habits of early Americans.' Britannica