Alright, here is the main text in question. Let's go through and put it as folks are suggesting on either side:
Mat 19:3 And Pharisees came up to him and tested him by asking, "Is it lawful to divorce one's wife for any cause?"
Mat 19:4 He answered, "Have you not read that he who created them from the beginning made them male and female,
Mat 19:5 and said, 'Therefore a man shall leave his father and his mother and hold fast to his wife, and the two shall become one flesh'?
Mat 19:6 So they are no longer two but one flesh. What therefore God has joined together, let not man separate."
Mat 19:7 They said to him, "Why then did Moses command one to give a certificate of divorce and to send her away?"
Mat 19:8 He said to them, "Because of your hardness of heart Moses allowed you to divorce your wives, but from the beginning it was not so.
Mat 19:9 And I say to you: whoever divorces his wife, except for sexual immorality, and marries another, commits adultery."
Interpretive version of those who think "put away" is equivalent to divorce:
Mat 19:3 And Pharisees came up to him and tested him by asking, "Is it lawful to divorce one's wife for any cause?"
Mat 19:4 He answered, "Have you not read that he who created them from the beginning made them male and female,
Mat 19:5 and said, 'Therefore a man shall leave his father and his mother and hold fast to his wife, and the two shall become one flesh'?
Mat 19:6 So they are no longer two but one flesh. What therefore God has joined together, let not man separate."
Mat 19:7 They said to him, "Why then did Moses command one to give a certificate of divorce and to divorce her?"
Mat 19:8 He said to them, "Because of your hardness of heart Moses allowed you to divorce your wives, but from the beginning it was not so.
Mat 19:9 And I say to you: whoever divorces his wife, except for sexual immorality, and marries another, commits adultery."
Interpretive version of those who think "put away" is not equivalent to divorce, and does not include an official certificate:
Mat 19:3 And Pharisees came up to him and tested him by asking, "Is it lawful for a man to put away without a certificate of divorce one's wife for any cause?"
Mat 19:4 He answered, "Have you not read that he who created them from the beginning made them male and female,
Mat 19:5 and said, 'Therefore a man shall leave his father and his mother and hold fast to his wife, and the two shall become one flesh'?
Mat 19:6 So they are no longer two but one flesh. What therefore God has joined together, let not man separate."
Mat 19:7 They said to him, "Why then did Moses command one to give a certificate of divorce and put her away without a certificate of divorce?"
Mat 19:8 He said to them, "Because of your hardness of heart Moses allowed you to put away your wives without a certificate of divorce, but from the beginning it was not so.
Mat 19:9 And I say to you: whoever puts away his wife without a certificate of divorce, except for sexual immorality, and marries another, commits adultery."
Just putting the proposed definitions into the passage, I am not sure I understand the second view. Especially troubling is this:
Mat 19:7 They said to him, "Why then did Moses command one to give a certificate of divorce and put her away without a certificate of divorce?"
It would make no sense for Moses to say "give her a certificate and send her away without a certificate".
Now if you divide the two into two distinct scenarios, it still does not make sense.
Why then did Moses command to give a certificate of divorce, and why did Moses command to send someone away without a certificate of divorce?
Moses did not command anyone to send away without a certificate of divorce. I just don't understand this view. Definitions of words have to still be considered in context.