With the exception of things like Alpha and Beta Radiation (which are respectivelly high energy atoms and neutrons, if I remember it correctly), all "radiation" (from to longwave radio waves, through infrared, visible light, ultraviolet, x-rays and into Gamma radiation) are ust photons with different energy levels hence different frequencies.
So the radiation from radars is just photons within a certain range of frequencies, which is even within what's considered the radio waves spectrum, same as a normal radio but of different frequencies hence different energy.
Radiation in this case is just used as a technical terminology (because they're radio waves that radiate from an emitter), same as one might say "microwave radiation" (which, by the way, is also just photon in a different part of the spectrum), rather than implying that it's the specific radiation from radioactivity.
There are indeed consideration in things like antenna design for different radio frequencies and you can't just design something that will work equally well for any of the entire range of frequencies. I was actually not thinking that HARMs could be "tuned" to different frequencies but rather than guidance module add-ons could be designed for more generic missiles in order to home in on specific frequencies for targetting jammers, as a jammer needs not be anywhere as complex as a radar and can be little more than a very strong emitter in a specific frequency or narrow range of frequencies which is emitting white noise.
(The idea of a GPS-guided missile with a terminal guidance module that just homes in on the strongest emitter in a certain radiowave frequency range is just delicious. I believe the Ukranians have used things like mobile phone emissions to locate and target Russian troops so they're at the very least manually doing triangulation of radio emissions)
From my naive knowledge from the side of Electronics it seems it would be reasonably simple to design a directional radiowave detector for what is the equivalent of "a guy shouting really loud to drown all conversation".
PS: But yeah, beyond all this, your point about specifically the HARM still makes absolute sense.