"Built-in" originally meant that the content came with the game itself. This category now also includes packaged DLC downloaded through the in-game systems. This content is packaged in a platform-specific format which is efficient for in-game use and which minimises disk size, but which typically lacks source textures and other such files that you'd probably want if you were editing or redistributing the content.
"Base" is a very small subset of the content included in the game, which is considered fundamental content that the game requires for correct operation. This content often has additional restrictions (such as not being possible to edit).
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