"...but mommy I just want to be with you. Just the two of us, please understand."
In Game
Alessa
Alessa of the game is vastly different that of the movie, especially in terms of her relationship with her mother. This version of Dahlia's daughter is the container of half of Samuel's soul, a fallen angel or "old god". She is viewed as a puppet with little or no uses since she is only half complete. Alessa was tortured by her mother, Kaufman (her father), and their cult by being burned a live in their family house and was kept alive in the bottom of the Town hospital. It was Lisa Garland's job to keep her 'alive'.
Cheryl
Cheryl Mason's birth parents are unknown, but perhaps the mother is Dahlia since she is the true mother of Alessa. She, like her adopted father, was drawn towards Silent Hill, only she was beckoned towards the other half of her soul who laid in hiding in her broken mortal shell.
Cheryl never seemed to be seen by the monsters, or see them, in the misty Silent Hill town reality. It is probably a reality where Alessa's power may have created in protection for them both. She is missing part of Alessa and only together they are whole. It is Dahlia's desire to unite them.
Movie
Alessa
Alessa is the fatherless child of a beautiful woman, Dahlia. She and her mother live in Silent Hill, where a cult controls most of the town's people. Alessa seems like a sweet child, loved by her mother, however her mother was forced into surrendering her child to the cult because they viewed the child as a Sin-incarnate.
She was tortured by the people by being burned as her mother sought to get her help. Her help arrived too late, the child condemned to the hospital like the game version of her was, and Alessa made a deal with something which changed her into a powerful entity. It seems she was normal child at birth and only inherited her powers through her suffering by the cult.
Sharon
Sharon is the adopted daughter of da Silva family. Rose, her mother, is the one desperately seeking her child in the misty town of Silent Hill. Sharon, before their arrival to the town, had nightmares and drew macabre artwork of the town.
Sharon, different from Cheryl, is actually what was left of the goodness in Alessa after her burning by the town's cult. She is not half of Alessa, only a piece of her.