Fruit is both a countable and uncountable noun in English. The plural of fruit is is actually still "fruit". The only time we would use "fruits" is when referring to different kinds of fruit (apples, strawberries, bananas). Either form of "fruit" or "fruits" would work in this example sentence, but as a native speaker I can say that "I want dried fruit" definitely is more natural and is used more often. Necer the less, this us a Hebrew course, not English. And the awkward English sentences help me remember things.
Technically it can mean both, and there is no other way to say your latter meaning. Then again, your latter meaning is... not very likely, is it? (Yes, I can imagine the scenario with the fruit stall in the market, in the rain...). So your former meaning jumps to mind more easily.