The word biscuit (from the Middle French bescuit) comes from the latin words bis (twice) and coquere or coctus (to cook, cooked), and hence means "twice cooked". As the original biscuits would be first baked then oven dried, this explains the name. By the time of the 14th century, the world bisquite was being used in England to refer to a hard twice-baked food item.
Cookie comes from the word koekje ("little cake") that was adopted by the Dutch in the 18th century to refer to a similar type of twice-baked foofstuff.
When Europeans started heading across the pond to the US, both words went with them. It was after the US War of Independence that cookie was adopted to refer to hard, baked products.
I would argue though that biscuit is the correct term as it is the one that was in use first. What Americans call "biscuits" should be referred to as bread - as this is what it is (just risen with baking powder rather than yeast). This is confirmed by the fact that they are often eaten with butter (like other forms of bread) and often at breakfast with something sweet such as jam or honey.
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