There are multiple planets in the Nintendo Universe. The two "main" planets, for the purposes of storylines are Planet Earth, and the separate, as of yet unnamed planet that has the continents Kremella, Elibe, some big Kong-esque continents, and probably tons of islands. Planet Earth is basically just like our normal Planet Earth, in physical structure anyway, but it has lots of psychic power and is populated with loads of Pokemon.
As far as Bowser and the Koopas are concerned: It was my original intent to have them exist in the "Dark World," that has been a big part of the Legend of Zelda series. If you do some research on the character the "Koopa Kingdom" has also been referred to as the "Dark Land" or "Dark World," already in some Mario games, so it's not much of a stretch. You may recall that the last several levels of Super Mario Bros 3 were within this "Dark World" and sometimes you literally couldn't see anything because the areas were pitch black.
The Dark World would be another alternate dimension, possibly a variant of the Plane of Shadows, that, like Kirby's Dream Land, overlaps with, and is coterminous with the material plane. Unlike the Realm of Dream, the Dark World that Bowser is from is much less connected to the material plane and it requires powerful magic and/or rituals to cross over into.
My plans for Ganondorf were that he was originally from a desert nation on the Elibe continent, part of the Fire Emblem kingdoms, and in his ambition to unite the Fire Emblem kingdoms under his own rule he sought out and obtained powerful black magic from the Dark World. In so doing, it is likely that he made enemies of Bowser and his legions.
Ganondorf is not necessarily an evil man. He wishes to unite the Fire Emblem kingdoms to provide harmony, economic stability, and an end to all of the major wars that seem to break out anew everyday. He harbors nothing but contempt and anger toward the Hyrulians who have been keeping him from seeking power through the Realm of Dreams. It is quite possible that he believes the world would be a better place without the presence of Hyrule.