imo LGPE did a bigger disservice at creating Green, a different character who's not Leaf and adding up the confusion. Also, her "personality" is just throwing pokeballs at you (oh did i say throw? what I mean was the screen going white multiple times)
Oh boy, this.
NOTE: Before I begin & anyone points it out, yes, in Japan the original games were Red & Green thus, in the Japanese versions, Blue & Green names are swapped; for the purpose of this post I'm using the name Green when referring to the Leaf "counterpart" in LGPE since I'm from the US.
I think it's mostly agreed that Green & Leaf are the same character even if unofficially confirmed. Nowadays, when it's not a duo picture of Red & Blue, its one or the other shown with them when doing a Kanto Trainer Trio shot. I think it's most notable in Masters which has Leaf but not Green, BUT Masters also includes Kris and Lyra confirming them to be different characters. Also the Special/Adventure Manga just keeps her as "Green" as they technically introduced Green first (though the manga also does a strange thing where they
made Kris wear Lyra's clothing for the HGSS arc thus combining the two characters, weird).
So, why did they have her as "Green" in LGPE? Well, my guess is to simply match with Red & Blue. Green/Leaf did not exist in Gen I and they never planned on having a choice of playable character.
Sugimori confirmed this himself, explaining that Green just existed as a quick girl trainer he included on the cover at for the Gen I guidebook so that they could have all Starters with a trainer facing each other on the cover; she didn't even have a name then. This girl design would then later be used as the basis for Green in the Manga. When they made FRLG, Sugimori said they did take her into consideration which I guess means they made her have the same hair style & color. They gave her the name "Leaf" as I guess a way to point out that, yes, she's a Kanto protag BUT was introduced later on in the remakes (obviously the manga didn't care, only doing a little joke when they had a practice battle where Red & Blue (who, remember, is called Green in Japan) swapped their Starters (Venusaur & Charizard) and a character commented it was a battle between "FireRed & LeafGreen"). Anyway, her officially being called "Leaf" didn't really matter as she was never given an NPC role in the games unlike Red & Blue thus her identity was whatever the player named her just like Red & Blue.
Now we've come to LGPE. They decided to introduce new protags and rival which freed up Red & Blue being their own NPCs (well, Blue at least, Red was still as reclusive and stoic as ever). However, this gave them also a chance to officially include the third Kanto trainer, the girl whom manga's Green & FRLG's Leaf was based on. But, being these games were marketed toward kids who may not know the complex history behind this character, and maybe a nod to the manga, they decided to name her "Green" so that you would know she's meant to be a trio with Red & Blue, having the Blastoise.
I guess we now come to the personality issue. Those who played Masters will note that Leaf does not act like Green who is a bit weird. To that, I say just a result of LGPE taking place in its own continuity. With the change of protags and rivals, that also changed Red & Blue's roles with Blue being more friendly & a helpful mentor toward the player & rival (infact, Blue
never even mentions or hints toward Red in the game). So I wouldn't take the odd behavior of Green in these games as meaning her and Leaf are unrelated counterparts of the same character (though maybe expect one day in Masters for Leaf to have a strange moment mentioning how she was younger she would try catching "people" and throwing Poke Balls at them).
Now with all that explained, have fun reading the arguments about Leaf & Green on Bulbapedia's discussion page for the characters.
Leaf has the majority of them, while the only one Green has
is asking why her page was split into its own thing, lol.
