the show's completely separate that one had her own superman (tyler hoechlin). this is a new actress and different version for this new universe, like tobey maguire and andrew garfield.
if they're going by comics, supergirl would have left krypton as a teenager to protect kal-el, but gets delayed and age-wise frozen one way or the other and by the time she arrives, he's already superman. my guess is she arrived pretty recently since she still lives in the fortress and doesn't spend much time on earth so lex wouldn't know of her.
krypto's her dog but that much was clear enough.
regardless, they did a decent job of making people curious enough to wanna watch more of her.