They are interchangeable synonyms.

They are sometimes used as synonyms but there is a slight difference in meaning. 'Prohibit' is used when something is not allowed because there is a rule/regulation/law against it. 'Forbid' is used when something is not allowed but there is not necessarily an official rule/law against it. E.g. Smoking is prohibited in this restaurant BUT My mum forbade us from smoking in the house.