Is Moderance a temperance?

Temperance in its modern use is defined as moderation or voluntary self-restraint. It is typically described in terms of what an individual voluntarily refrains from doing. The term "temperance" can also refer to the abstention from alcohol (teetotalism), especially with reference to the temperance movement.

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And another question, why did temperance supporters ban alcohol?

The temperance movement had popularized the belief that alcohol was the major cause of most personal and social problems and prohibition was seen as the solution to the nation's poverty, crime, violence, and other ills. Moreover, why did the temperance movement ban alcohol? The goal of the temperance movement in the United States was to make the production and sale of alcohol illegal. Supporters believed that prohibiting alcohol would solve a number of society's problems, making people safer, healthier, and more productive.