Ibrahim bin Sa'd (may Allah have mercy on him) asked Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) about a woman whose husband divorced her twice and who then took khul' from her husband: may the husband marry her? Sayyiduna Abdullah bin Abbas (may Allah be pleased with them both) said: Allah mentioned divorce at the beginning of the verse and at its end, and khul' is mentioned in between; so khul' is not divorce, and he may marry her.
(b) Amr (may Allah have mercy on him) narrates from Ikrimah (may Allah have mercy on him): Everything that is made permissible through wealth is not divorce.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الخلع والطلاق / 14863