What is the difference between permissibility (ibāḥah) and innovation (bidʿah) in Islamic legislation, and what is the relationship between them?

The permissible (mubah) is that which Allah has permitted to be done or left without dispraise or praise. It is permissible to do or leave it without any reward or punishment being incurred. As for innovation (bid'ah), it is an invented way in religion that parallels the Sharia. It must be abandoned, and it is forbidden to do it. Its doer is punished, and its abandoner is rewarded. The permissible may be rewarded if its doer intends it as an act of drawing closer to Allah.