If the second type of information isn't explicit or implied, then it might be described as inferred information. But neither implied nor inferred suggest motivation or existence specifically. Existential might suggest both, depending on your understanding/belief of what existentialism is about.

If the appropriate word isn't well known, with clear and common understanding, to people generally, then whatever word you choose will probably require a definition in the context. If you are going to define your term, it doesn't matter much what it is, but there might be value in choosing a term that isn't loaded with confusing/confounding meanings among your readers. You might call it "red information", with an appropriately verbose definition of what you mean.

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