Narrated Ibn `Abbas:
For the children of Israel the punishment for crime was Al-Qisas only (i.e., the law of equality in punishment) and the payment of Blood money was not permitted as an alternate. But Allah said to this nation (Muslims): 'O you who believe! Qisas is prescribed for you in case of murder, .....(up to) ...end of the Verse. (2.178) Ibn `Abbas added: Remission (forgiveness) in this Verse, means to accept the Blood-money in an intentional murder. Ibn `Abbas added: The Verse: 'Then the relatives should demand Blood-money in a reasonable manner.' (2.178) means that the demand should be reasonable and it is to be compensated with handsome gratitude.
Narrated Ibn `Abbas:
The law of Qisas (i.e. equality in punishment) was prescribed for the children of Israel, but the Diya (i.e. blood money was not ordained for them). So Allah said to this Nation (i.e. Muslims): "O you who believe! The law of Al-Qisas (i.e. equality in punishment) is prescribed for you in cases of murder: The free for the free, the slave for the slave, and the female for the female. But if the relatives (or one of them) of the killed (person) forgive their brother (i.e. the killers something of Qisas (i.e. not to kill the killer by accepting blood money in the case of intentional murder)----then the relatives (of the killed person) should demand blood-money in a reasonable manner and the killer must pay with handsome gratitude. This is an allevitation and a Mercy from your Lord, (in comparison to what was prescribed for the nations before you). So after this, whoever transgresses the limits (i.e. to kill the killer after taking the blood-money) shall have a painful torment." (2.178)