Rinoa is Ultimecia but with Adel's memories and GF poisoning ruining her true memory. She was junctioned onto Adel and absorbed some of her memories, her use of GF (as a civilian) was probably more destructive and ruined her true memories of what happened, and also the following:
To start off, I found it odd that in between the speech during Deling City and the CG cut scene, there is a short scene were the screen turns black when Rinoa is standing dizzily next to Ultimecia in Edea's body. Ominous 'succession of the witches' music is all over the place as if to hint at something evil. The speech itself is about the witch that they all fear.
In the Orphanage reveal, Rinoa makes a small comment about how she cannot keep up with the rest of them but tries her best. GF contamination is revealed. The rest of them are all trained soldiers with experience regarding G Fs and even they suffer severe memory loss. Rinoa is not a trained soldier and her body cannot deal with it as well as the others.
Much later, Squall gives his ring to Rinoa during the battle of Gardens and your allowed to name the GF but you can't ever use it. I found that really odd. Edea reveals that Ultimecia from the future desires to change the past because of 'something bad' that happened. During this, all Squall thinks about is Rinoa while Edea talks about Ultimecia and tragedy.
Rinoa is taken over for the specific purpose of breaking open Adel's seal. Rinoa's space suit is running out of oxygen and Squall's ring is shining after the oxygen is apparently all gone. I inferred that the ring was a GF. Squall saves her and they get onto Ragnorak. After you beat all the monsters, Rinoa talks about how she wants 'Time to stand still' and how she 'Doesn't want the future'. She just wants to stay with Squall. Squall later saves her from being sealed the same way Adel was.
Laguna explains Adel's sealing and how Adel probably wanted Ellone as a successor. That was why Adel had soldiers kidnap Ellone. It's mentioned that Adel's 'Will' is stronger than Ultimecia's.
In the orphanage scene where Squall tells Rinoa that she will find him at the orphanage if he goes missing... Rinoa proposes the idea of if she became an evil sorceress. She talks about how she would be okay if it was Squall who killed her. She specifically mentions words along the line of how 'Squall's sword will pierce my heart, it'll be okay if it's you, Squall'. Squall is the designated 'Legendary See D' who is suppose to vanquish Ultimecia. Afterwards, Edea gives words of dark inspiration. 'You must fight to the end! Even though it may bring tragedy to others!'.
The cut scene where Adel junctions Rinoa onto herself. The music 'A Sacrifice' plays. After you beat her, Rinoa mentions something a bit frightening. 'I was inside a young Adel'. Remember Adel's goal? She wanted a successor. Do you remember the words on the radio tower? It was jumbled up but one of them said 'I will never let you forget about me'. Those were Adel's thoughts. Adel's name is unisex but the female derivative translates to 'God is Eternal'.
Ultimecia, for no reason at all, summons the most powerful GF and it has the same name as Squall's ring. A ring which Rinoa is carrying. Ultimecia's in-game design is the complete opposite of Rinoa's (on purpose) and very similar to Adel's.
Now, I assumed that a lot of the game was foreshadowing and never explicitly stated it, just like they never explicitly say that Laguna is Squall's father (and remember their designs were made opposite on purpose), but I assumed the following:
Adel put some of her earliest memories into Rinoa during the junction because she didn't want to be forgotten about and saw Rinoa as the perfect opportunity. Rinoa was not a capable soldier who could resist Guardian Force contamination as well as the others. Rinoa had Squall's ring with her throughout much of the journey.
Somehow, she lost her memories and one day 'woke-up' believing herself to be Adel. The 'event that Ultimecia wished to change' was Laguna trapping Adel into the Seal. Adel wanted vengeance and Ultimecia wanted to live on eternally. It fit with Adel's defined name meaning 'God is Eternal' and Ultimecia's actual translated name being the Goddess Artemis. Artiemis is the goddess of the moon, the hunt, the cycle of re-birth and death (this is lesser known), and many other things.
On the off chance they ever start working on an FF 8 remake like they did with 7, let's put a section in here.