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Managed Metadata column
The Managed Metadata column is a new column type that can be added to lists or libraries so that site users or content owners can select values from a specific term set of managed terms and apply them to content. A Managed Metadata column can be configured to map to an existing term set, or you can create a new term set specifically for the column. If you create a new term set specifically for a Managed Metadata column, that term set will be a local term set that is available only for use within the site collection where it was created.
Taxonomy
A taxonomy is a hierarchical classification of words, labels, or terms that are organized into groups based on similarities. A taxonomy may be defined and centrally managed by one or more individuals. The International Standard Industrial Classification (ISIC), which was developed by the United Nations, is a famous example of an industrial taxonomy that is used to classify economic data. Taxonomies are useful because they provide a logical, hierarchical structure of metadata that can be used to classify information consistently.