Are snakes and earthworms from the same species?

They are not even remotely close! They are both types of animal (kingdom Animalia), and that's about the closest relationship you can describe. Earthworms are annelids (phylum annelida), a kind of invertebrate, while snakes are reptiles (phylum chordata, class reptilia), which are vertebrates. Each of those types of animals has multiple species that are collectively given the name earthworm or snake.

https://en.wikipedia.org/wiki/Earthworm

https://en.wikipedia.org/wiki/Snake

Back in the days when whales were fish and the giraffe was a cross between the camel and the leopard, the term 'worm' was applied to almost anything that was long, thin, and wriggly. Back then, too, the word 'species' had a simpler meaning - something like 'a kind of''. So both snakes and earthworms were 'worms' as they were long, thin, and wriggly. I don't think that eels were, though, as because they lived mostly in the water they had to be fish. It was when science started sticking its nose in everywhere, and making unnatural claims that whales weren't fish after all, and that having a backbone or not was more important than being long, thin, and wriggly or not, that snakes and earthworms were separated in most people's minds. The application of 'worm' to dragons has changed in modern usage, and it has become 'wyrm' (pronounced the same as 'worm') in most modern fantasy. It looks better, too, and more antique (which it actually is...), and is probably more acceptable to the dragons themselves (or at least to those who would support ethical treatment for them). https://en.wiktionary.org/wiki/worm#English