Kore is the same character as Persephone in Greek mythology. The story goes that Persephone/Kore was the daughter of Demeter, the goddess of agriculture. Hades kidnapped her, and she became the queen of the underworld after eating six pomegranate seeds. (source)
Her mother was so distraught at her daughter’s absence that she did not help the plants grow. A compromise was made that Persephone would spend six months in Hades, one for each seed she ate. The rest of the year, she would spend with her mother. This division of time is used to explain the scarceness of some seasons and the lushness of others.
This figure may have multiple names for a few different reasons. In some versions of the tale, she is referred to as Kore before her abduction and Persephone after. It is also possible that this figure is the conflation of a few similar figures, including Kore and Persephone. Different sects of the Hellenic religion may prefer one name over the other.