What is the difference between Khamr (wine/intoxicant) and alcohol, and what was the nature of the vinegar that the Messenger, may Allah bless him and grant him peace, loved, and was anything added to it to purify it?

It is authentically reported in the Sahihayn from Aishah that the Prophet, peace and blessings be upon him, said: "Every intoxicant is khamr (wine), and every khamr is forbidden." In al-Bukhari: "Khamr is that which clouds the intellect." And alcohol is an intoxicant, so it is khamr.

As for vinegar made from khamr, it is that which has fermented on its own, based on the Prophet's, peace and blessings be upon him, saying when asked about khamr being made into vinegar: "No."

The vinegar that the Messenger of Allah, peace and blessings be upon him, loved was vinegar that was not made from khamr. There are no hadiths stating that the Messenger of Allah, peace and blessings be upon him, would add anything to vinegar to purify it; rather, what is reported is the prohibition of fermenting khamr into vinegar.