Put away and divorce are the same thing, the Pharisees are just summarizing what Moses said.
Mark 10
2 And the Pharisees, having come near, questioned Him if it is lawful for a husband to put away a wife, tempting Him
4 And they said, “Moses permitted to write a bill of divorce, and to put away.”
Deuteronomy 24
1 then he has written a writing of divorce for her, and given [it] into her hand, and sent her out of his house;