According to people who deal in fruits and vegetables at the market, vegetables are eaten as a side dish with rice, while fruits are eaten as a snack or dessert.
This is a very simple classification, but it seems to be the only way to distinguish between vegetables and fruits at present.
The distinction between vegetables and fruits is not based on the characteristics of the plant or the way it is cultivated, so there is no very precise way to divide the two.
Watermelon is not usually eaten with rice. Therefore, watermelon should be considered a fruit.