From A Wiki of Ice and Fire
When asked about this discrepancy George R. R. Martin simply said that Sansa is an "unreliable narrator". This has led to much speculation by fans on what he means and intends.
See also: Main article: Sansa Stark/Theories
A Clash of Kings
Sansa eventually arrives. The Hound is very drunk, drunker than she had ever seen him. He offers to take Sansa with him as he intends to flee the city. He mentions going north somewhere. She refuses. He pushes her on her bed holds a knife to her throat and drunkenly demands that she sing him the song that she had promised him earlier. She sings, but not the song of Florian and Jonquil. Instead a terrified Sansa sings the Mother song:
|“||Gentle Mother, font of mercy,
save our sons from war, we pray,
stay the swords and stay the arrows,
let them know a better day.
Gentle Mother, strength of women,
help our daughters through this fray,
soothe the wrath and tame the fury,
teach us all a kinder way.
The Hound falls silent and Sansa gently touches his cheek feeling the wetness that was blood and the wetness that was not blood (tears). Shortly thereafter he gets up, rips off his bloody white cloak, and leaves. Sansa shakes out the torn and bloody cloak and huddles beneath it shivering. Ser Dontos Hollard eventually comes to tell her the city is saved.
A Storm of Swords
Sansa comes to remember this scenario slightly differently, remembering that the Hound also kissed her.
Sansa remembers the (un)kiss:
|“||Megga couldn't sing, but she was mad to be kissed. She and Alla played a kissing game sometimes, she confessed, but it wasn't the same as kissing a man, much less a king. Sansa wondered what Megga would think about kissing the Hound, as she had. He'd come to her the night of the battle stinking of wine and blood. He kissed me and threatened to kill me, and made me sing him a song.||”|
In contrast as he lies dying Sandor thinks of the song Sansa had sung to him and tells Arya Stark:
|“||And the little bird, your pretty sister, I stood there in my white cloak and let them beat her. I took the bloody song, she never gave it. I meant to take her too. I should have. I should have fucked her bloody and ripped her heart out before leaving her for that dwarf.||”|
Feast for Crows
|“||As the boy's lips touched her own she found herself thinking of another kiss. She could still remember how it felt, when his cruel mouth pressed down on her own. He had come to Sansa in the darkness as green fire filled the sky. He took a song and a kiss, and left me nothing but a bloody cloak.||”|
|“||File this one under "unreliable narrator" and feel free to ponder its meaning...||”|