Difference between Divorce & Khula

Talaq (Arabic: الطلاق‎) is the Islamic term for divorce. A talaq is used to end a marriage, or nikah, under the terms of Islamic sharia. It should be noted that Talaq is a right given by a Husband and Wife can only exercise the right of Talaq if the same is granted to her in her Nikkahnama (Marriage Contract). If the Husband gives Talaq he must also tender Haq Meher to his Wife, whereas if the Wife excercises her right of Talaq then she must relinquish her right to Haq Meher.
It is important to note that Shia and Sunni Muslims have different rules for performing a Talaq. Sunni practice requires no witnesses, and allows a husband to end a relationship by saying the triple talaq, whereas Shi'a scholars view the triple talaq (in one sitting or at one time) as ajahiliyya a custom, forbidden by Muhammad, but reinstated by Umar ibn al-Khattab, and thus  forbidden. Sunni scholars agree to the facts, but deem it halal ("lawful") anyway.

Khula (Arabic:خلع) is the right of a woman in Islam to divorce and it means separation from her husband. After divorce, the husband is responsible for the education and maintenance of the children. The children live with the mother till the age of Hizanat which is seven years for son and age of puberty for daughters.
 After the age of Hizanat, the children have the right to live with the father or the mother, and their opinion will be considered by the court but will not be taken as conclusive and decisive factor.
A woman seeks a Khula while a man seeks a Talaq. The Iddah period also allows for reconciliation for the husband and wife.

• According to Surrat al-Baqarah - Verse: 229 (( Divorce may be (pronounced) twice, then keep (them) in good fellowship or let (them) go with kindness; and it is not lawful for you to take any part of what you have given them, unless both fear that they cannot keep within the limits of Allah; then if you fear that they cannot keep within the limits of Allah, there is no blame on them for what she gives up to become free thereby. These are the limits of Allah, so do not exceed them and whoever exceeds the limits of Allah these it is that are the unjust ))