1. An apple floats on water.

2. A coin sinks in water.
3. An apple floats on the water.
4. A coin sinks in the water.
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In #1 and in #2, 'water' is in generic use, right?
What about in #3 and #4? What is the difference?

I don't see much difference between "on water" and "on the water" -- unless (in 3 and 4) you're referring to a particular body of water, such as a lake or a bathtub.