secretus

Secretus, secreta, secretum is the perfect participle of secerno, "to set apart" - se- plus cerno, "sift". So the base sense is separated, and secrecy is only what follows from being kept apart from other people. Read it that way and the classical uses stop looking odd: locus secretus is a remote spot with nothing furtive about it, and secretus a vulgo means simply "away from the crowd".

The neuter noun secretum, "a thing set apart", gives medieval Latin secretarius, the official trusted with the private correspondence, and from him English secretary - a job title that still admits what it was for. The adverb is secreto, "privately". Distinguish occultus, which is hidden by concealment, and arcanus, which is hidden because it is sacred.