A/N: Sasha/Cat is an original character of mine, intended once for a big story which was never written. Instead, recently, the concept came back to life with a plotbunny.
Sasha is not related to any canon character, especially Selina.
Batman Is Batman
Batman likes dark nights, isolated rooftops, mysteries to solve, secrets to uncover, solitude to live in and all the rest of those gloomy things. He's indifferent to Cat's advances, and his little jabs, and his stupid jokes, and his cheery carelessness.
Batman doesn't care about little things. He hates the distraction.
Terry, on the other hand, cannot help but smile when Sasha laughs, and tells him the latest gossip, and tries to feed him his lunch, and simply is who he is.
All of this because Batman is Batman, Terry is Terry, and Sasha… No matter what, Sasha is Sasha.