Within the regulatory authority of the U.S. Food and Drug Administration, radiation-emitting product has a specific technical and legal meaning. There are a great many products that emit ionizing radiation and non-ionizing radiation, but that come under FDA jurisdiction they meet the technical definition and make claims that they provide health benefits.
The FDA authority comes from Section 531 of the Federal Food Drug & Cosmetic (FD&C) Act. It begins with defining electronic product radiation as "any ionizing radiation or non-ionizing electromagnetic energy or particulate radiation" (see neutron, electron, positron, photon, proton or alpha particle," or produces "any sonic, infrasonic, or ultrasonic wave",
Such waves and particles, as covered here, come from an "electronic product" that is "any manufactured or assembled product which, when in operation, contains or acts as part of an electronic circuit and (ii) emits (or in the absence of effective shielding or other controls would emit) electronic product radiation," or "any manufactured or assembled article which is intended for use as a component, part, or accessory of a product described in [the preceding clause]] which when in operation emits (or in the absence of effective shielding or other controls would emit) such radiation;
According to the FDA, radiation-emitting products come under its jurisdiction "if you make any medical claims, your product is a medical device also subject to the provisions of the FD&C Act for medical devices in addition to the provisions for radiation emitting products."
Other government regulation
Sources of ionizing radiation or particles also may be under the jurisdiction of the U.S. Department of Energy, and possibly state and local agencies.