You are confusing a type of data with a storage location.
Metadata is "data about data." The picture information is your data, the caption is metadata.
Metadata such as captions can be saved in one of three locations- part of the photo file itself, in a secondary, linked (sidecar) file, or in either a system-level or application-level database. Which one(s) are used depends on the file type and application settings.
As an example, a JPEG file would typically store metadata in the file itself and/or a database. But a RAW file would store metadata in a sidecar file and/or a database.
Check the Elements and Lightroom documentation to see how to control where metadata is stored.