The word "berry" goes back to proto-Germanic. Outside the context of botany, it means "small fruit". (And even in the 9th century, it meant "small fruit", though at the time it was more strongly associated with grapes than it is now.)

Carl Linnaeus lived in the 18th century. The botanical sense of "berry" developed from the ordinary sense -- almost certainly because someone was investigating "what do all these berries have in common?", and picked a trait that identified the largest number of small fruit.

You can see the same thing happening with "fish". Starfish and jellyfish are not "fish" in a taxonomic sense, but they are things that live in the water. In Chinese, octopuses and crocodiles are also "fish". (章鱼 and 鳄鱼, where 鱼 by itself is "fish".)