Do you have to separate watermelons (Citrullus lanatus) from other types of melons to keep them from cross-pollinating?
No, other types of melons like cantaloupes or honeydew (Cucumis melo), and cucumbers (Cucumis sativus) can all be grown close together without fear of crossing. However, each of these items will cross within their own species.
So, if you wanted to save seeds from the fruit to plant next year, you would need to separate different varieties of watermelon from each other (or different varieties of melons or different varieties of cucumbers).
When a cross does happen between two varieties within the same species, the resulting fruit that year is completely normal looking and tasting. Only the resulting seed carries the crossed gene. So, if you saved the seed and planted it the following year, you might get something of a cross between the to varieties.
If you are growing any combination of watermelons, melons, or cucumbers to eat the resulting fruit, you do not have to worry about cross-pollination in your home garden.