A message beneath a message is labelled as

A hidden or underlying meaning beneath a stated message is called subtext.

Embedded text is text placed inside another file or object, a different idea.

Internal text is not the term for a hidden meaning.

Intertext refers to links between different texts, not a buried meaning.

Subtext carries what is implied rather than openly stated.

Add-on: recognising subtext is important in media and communication analysis.