A message beneath a message is often referred to as

A message beneath a message is often called the sub-text.

It is the underlying, implied meaning that runs below the surface words of a communication.

The receiver reads it between the lines rather than from the plain, stated content.

Lower text is not a recognised term for this hidden layer of meaning.

Critical text points to writing that analyses or evaluates, not to a concealed inner message.

Appended text means matter added on at the end, the opposite of a meaning buried within.