Here’s what I’m gleaning, upon considering the most popular answer and additional resources:

• $tag seems to be a synonym for the name of the hook. (That’s not particularly intuitive to me.)
• the_content is an example of a hook, of the “filter” type.
• the_content hook consists of multiple filters.
• Filters modify data. They basically filter the database, changing the data before the users view it.
• A common use of apply_filters(), for instance, is to apply the_content filters to $content. In this instance, double returns will convert to <p> tags, smiley faces will convert to icons, etc.
• “the_content” is a hook, while “the_content()” is a function.

NOTE: This answer was originally posted at StackOverflow.com by Marjorie Roswell