Is the alcohol found in some foods—such as vinegar or mustard—the alcohol forbidden by Sharia?

Vinegar mixed with alcohol is forbidden to use unless the alcohol has undergone a transformation.

If the presence of alcohol in vinegar is confirmed, its use is forbidden until its transformation is established. However, vinegar found in Muslim markets, where its transformation into alcohol is not known, remains pure.

The preceding discussion pertains specifically to intoxicating alcohol, because not all alcohols are intoxicating.

As for previous use of a product containing alcohol without deliberate intent, there is no blame for it, based on the saying of the Prophet, peace and blessings be upon him: "Indeed, Allah has forgiven my nation for mistakes, forgetfulness, and what they are forced to do."