Arceus was born from an egg in a void. It created Dialga, Palkia, and Giratina to represent time, space, and antimatter, AKA existence. It created Uxie, Mesprit, and Azelf to represent knowledge, emotion, and willpower, AKA spirit.
Groudon was created from pressurized magma deep within the planet. Kyogre was created from pressurized water deep within the oceans. As they traveled, they expanded the land and oceans, and eventually came into contact with one another, sparking a rivalry. Rayquaza was formed from minerals in the atmosphere.
Mew is thought to be a common ancestor to all Pokémon because it is capable of learning just about any move taught to it, though this became less and less true as the games progressed and signature taught moves became a thing.
Mewtwo is a clone of Mew.
Deoxys is a mutated space virus.
Ultra Beasts are Pokémon that originated in different dimensions accessed through Ultra Space.
Some Pokémon are just really rare and powerful to the point they're called "Legendary", like Articuno, Zapdos, and Moltres. There's nothing saying that more than one can't exist. Like you can only find two Snorlax in Kanto, but that doesn't mean only two existed in the entire world. Genders and breeding didn't exist in Gen I either, so it's not like it was really any different to Legendary Pokémon.
Mythical Pokémon are Pokémon that are exceedingly rare to the point where people think they may not exist.
The second tier of Legendary Pokémon (the ones that appear on box art, along with Mewtwo, Zygarde, Cosmog, and Cosmoem) may be known about but their existence may be disputed unlike the first tier. Everyone accepts that Articuno exists, but Ho-Oh is a real legend.
