A field is a way to attach a piece of information to a specific asset. You can see all the fields on the right hand side when you're viewing an asset:

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You can read more about different types of fields here.

Filters are a way of narrowing down your search results to find the asset you need.

Filters appear on the side of the All assets and Browse pages. They allow you refine the search results either by choosing from your custom fields, or from built-in information such as file type or uploader.
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Yes, please refer to this article.