The other answers are currently just appealing to common definitions, but belaboring the point a bit further there's a real difference.
Imagine you hold your hand 1/4 inch above an electric stove on high. What do you expect to happen? You're pumping 1kw into your hand, so probably nothing good. What you don't expect from a duration of a minute or two though is much in the way of DNA damage. You'll mostly recover, give or take a bit of scarring and lower-probability acute health risks (even that scarring degrading to nothing over time if you're young).
Contrast that with 1000x less power (just 1 watt), but in the form of a focused x-ray. It can't affect many tissues, but the energy in each photon breaks chemical bonds the stove couldn't dream of in thousands of years. When using it as a diagnostic tool or a treatment, the best you can hope to do is mitigate the blast radius.
Some therapies are, by that definition, a bit of a hybrid. Binding nanoparticles to a tumor to excite them with near-infrared energy is pretty clearly a form of radiation, but the technique uses those wavelengths because they mostly just pass through your tissues and because it's easy to tune nanoparticles in those wavelengths. The effect on your body (beyond any cytotoxic effects of the particles) is a localized thermal treatment.
This new treatment is both non-radiative definitionally (using something other than the electromagnetic spectrum), but it fits into that last group of things, as a way to focus energy into problematic cells without letting stray high-energy particles cause excessive damage. Damage is limited to local thermal stresses, with probably some unknown unknowns with respect to cavitation inside blood vessels.
Sure, lots of things radiate, but the meaning is clear, no? The word ‘radiation’ without a qualifier or in a medical context is generally understood to refer to EM & particle radiation, such as x-rays, gamma rays, etc.
We’re slowly getting there:
https://www.fusfoundation.org/diseases-and-conditions/prosta...