Though, Kid is Schala, who grew up in a different surrounding. They are the same entity, and as it can be said "they are different people". That's the same as Magus and Janus. Magus goes up to Janus, Janus is like WTF, and Magus tells like Crono "I used to be different, didn't I".
Schala grew up differently, matured. Kid was cloned, grew up. Schala looks at Kid "Wow, you're a different person to me". They're mentally different... And physically only different by Scars that Kid has on her elbows and some white face paint.