M'kay so Sora is the main protaganist in the KH Games and his destiny is to visit different Worlds that are based off classic Disney movies (Tron, Mermaid, Mulan, Beauty & the best to name a few) and battle the evil characters of them. So you play through levels based on the Films, and defeat the evil characters inside them. Sora is a human and in the first Game after finding a certain item, adult Simba could be summoned to help attack enemies for a while, there was to be a Lion King level but it was scrapped because the Game's designer wasn't happy with the look of it so it was removed and worked on for the sequel (KH2).
In Kingdom Hearts 2 a new World was introduced called Pride Lands which as you'd imagine is a playable Lion King world with such areas as the Elephant Graveyard, Pride Rock and the Oasis (where Timon & Pumba take Simba). For this level Sora was transfromed into a Lion ( see my sig) version of himself (hence he still has his Necklace) and you play through TLK from the point where adult Simba is living with Timon & Pumba and Nala is about to find him. As adult Simba was available as a summon in the first Game, that is why the level starts from that point of the Film. You play through up untill you help Simba fight & defeat Scar (Kiara is not shown at all & Simba never has a Cub).
You do re visit the world later on, but the story is a completely new one where Simba is struggling to keep order as the new King.
Hope that has cleared it up a bit

Kiara is shown in KH2. Watch the credits.