"Ban" as a verb is the same as "prohibit," meaning to officially exclude someone or something: "The police are going to ban/prohibit the sale of alcohol on this beach." "Ban" as a noun is the same as "prohibition," a more formal or legal order of exclusion: "There is a ban/prohibition on the sale of alcohol on this beach."

They are close synonyms and are almost interchangeable. "Prohibition" sometime has a limited meaning: the prohibition of alcoholic beverages. In the United States, the word "Prohibition" with a capital P refers to the period of 1920-1933 during which the manufacture, transportation, and sale of alcoholic beverages was prohibited. It would be perfectly natural to say that "during Prohibition, alcohol was banned."

They are synonymous.