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The Johto trio are weird like that, they have two different and somewhat contradictory versions of their lore.
The first one is the most famous, the burned tower story where the three were died and were resurrected representing the elements of the event, the lightning that struck the tower, the fire that burned and the rain that put it out.
The second version is the stuff described in the Pokedex and occasionally alluded to in spin-offs. Entei is volcano god of sorts, Suicune embodies the cold, northern winds and Raikou is... mostly the same, a living lightning bolt.
What's interesting is that the latter version seems to have more in common with their designs, like Entei having a whole volcano motif on its back and Suicune's aurora-like mane and streamer tails. It's like the Johto legend was written after they were designed and their dex entries were finished and Game Freak never really tried to reconcile the two. Maybe they thought the beasts having different proposed origins was more interesting.
