The reason a design you liked is never lost.
A generative system makes thousands of tiny random decisions. If those came from genuine randomness, every design you liked would vanish the moment you refreshed the page. So generative tools use a pseudo-random number generator: a deterministic function that spits out numbers which look random but are entirely decided by one starting value, the seed.
Same seed, same stream, same drawing. Every time, on every machine, for as long as the code exists.
A design becomes portable. A generator id, a handful of parameter values, a seed and a palette are enough to rebuild the artwork exactly, which is why a link can carry a whole design without an image being stored anywhere.
Exploration also gets structured. Changing only the seed hands you a different draw of the same idea, so you can audition variants without losing the thing you spent twenty minutes tuning.
Decent systems do not run everything off one random stream. They fork it: one for positions, another for colour, another again per layer.
Skip this and you get the single most irritating failure in generative tooling, where nudging one slider reshuffles the entire picture because every downstream decision has shifted along the stream with it.
Is pseudo-random less random? For art, no. The numbers are well distributed. They are simply repeatable, and repeatable is what you want here.
Can two designs share a seed? Yes, and it means nothing. A seed only has meaning next to a particular system and its settings. The same number on two systems gives two unrelated results.