What is the difference between the permissible and the forbidden?

All perfect praise be to Allaah, The Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger. 

There is no connection between the permissible and the prohibited or forbidden. The permissible is what conforms with the sharee'ah. In his book Al-ʻIddah fee Usool Al-Fiqh, Ibn Al-Farraa' said, “The permissible is that which conforms to the sharee'ah. When we say that a prayer is permissible, or a fast is permissible, or a sale transaction is permissible, then we mean that it conforms to the sharee'ah.”

As for the prohibited, it is what the sharee'ah definitively forbade, as it has been defined by Al-Maaziri in his book Eedhaah Al-Mahsool.

Allaah knows best.