What difference would that make ? either way they are no longer together, it just lacks the STAMP.
Well two people who are no longer together but not divorced are in fact still married, and if you hook up with someone who is put away (not divorced) you cause that person to commit adultery.
Hypothetical: Brad and Jen were separated when Brad met Ang. Brad and Ang hooked up while filming a movie, and was in adultery as he was still married to Jen. The difference that a STAMP makes is huge in this case.
In the Jewish culture, the STAMP is even more important, as a Jewish woman could not get her life back as she was still tied to her husband. This in fact still goes on.
Now read the story Jesus spoke with a different translation, the ASV:
but I say unto you, that every one that putteth away his wife, saving for the cause of fornication, maketh her an adulteress: and whosoever shall marry her when she is put away committeth adultery.
A put away woman who violated the marriage covenant made the marriage null, therefore she could be put away without divorce, which is what happened in Ezra.
3 And there came unto him Pharisees, trying him, and saying, Is it lawful for a man to
put away his wife for every cause?
4 And he answered and said, Have ye not read, that he who made them from the beginning made them male and female,
5 and said, For this cause shall a man leave his father and mother, and shall cleave to his wife; and the two shall become one flesh?
6 So that they are no more two, but one flesh. What therefore God hath joined together, let not man put asunder.
7 They say unto him, Why then did Moses command
to give a bill of divorcement,
and to put her away?
8 He saith unto them, Moses for your hardness of heart suffered you to put away your wives: but from the beginning it hath not been so.
9 And I say unto you, Whosoever
shall put away his wife, except for fornication, and shall marry another, committeth adultery: and he that marrieth her when she is put away committeth adultery.
Ever wonder why this was a trick question asked to Jesus?