Sensing privacy and communication confidentiality play fundamentally different but interconnected roles in adversarial wireless environments. Capturing this interplay within a single physical-layer framework is particularly challenging in integrated sensing and communication (ISAC) systems, where the same waveform simultaneously serves dual purposes. We study a secure ISAC system in which a monostatic transmitter simultaneously sends a confidential message to a legitimate receiver and senses an environmental state, while a passive adversary attempts both message decoding and state estimation. We partially characterize the fundamental trade-offs among three performance measures: the transmitter's secrecy rate, its detection exponent, and the adversary's detection exponent. Beyond the joint input distribution that governs overall performance, the trade-offs are further shaped by the transmitter's ability to extract keys via feedback and hide both the content and structure of the codewords via wiretap and resolvability codes. We derive an achievable region, and illustrate the resulting design trade-offs through a numerical example.