Unfortunately Fate/stay night is one of 'those' games turned into an anime, but other than a few parts I don't think you could tell unless someone told you. The show is pretty good and not just full of fighting, I liked it a lot and I especially liked the character designs. The story follows one branch of the game's story, I forgot which one but overall the plot and characters are pretty good. I'd recommend checking it out if you're interested.
Oh and there actually is a little girl in the series but her role in the plot is pretty neat.
