The small flattish white seeds in a watermelon are undeveloped because they are not fertilised; the seedless melon cultivar is grown from seeds, but these seeds are the result of a specific cross-pollination between two different varieties (or perhaps species) that happens to result in infertile offspring.
Members of Cucurbitaceae will often form fruits even if pollination fails (if the cucumbers you buy in the supermarket had been pollinated, they would be curved and very bitter).
Many other seedless fruits (such as grapes) are either propagated from cuttings originating from a mutant, non-seeding strain (which would quickly have otherwise died out), or are the result of ordinary plants being treated with the right hormones to promote fruit development in the absence of pollination.
Most of the time, seedless fruits are aneuploid - that is, they have an odd number of each chromosome. Humans are diploid, meaning we have two of each chromosome. Modern commercial strawberrys are octoploid, and so on. When the number is even, chromosomes can pair up nicely during meiosis and everything goes well. When the number is odd, you end up with extras of some chromosomes and shorted on others, so gametes die quickly instead of forming fully. White watermelon “seeds” are, in fact, abortuses. I can’t remember what ploidy seedless watermelons are offhand. I want to say they’re pentaploid, but I’m not sure. I know bananas are triploid, though, which is why you just get those little black specks instead of marble-sized seeds.
I asked this question looooooooooooong ago.
After years of buying “seedless” watermelons I’ve found that those that are very ripe have no seeds. Zero. Not even the white ones. Now why is that? Explain why ripeness=no seeds at all.
Let me tell you, a ripe melon with absolutely no seeds is pure extacy.
This 4th of July weekened I juiced half of a ripe seedless and froze the juice into popcicles. Indescribable flavor!