It is a matter of confusing terminology , at the present times when so much differentiation has happened in physics related scientific disciplines.
Radiation was a general terminology assigned to transfer of energy radially, to start with with waves: acoustic waves, waves in water.
Then came Maxwell's equations and the discovery of electromagnetic waves, which emitted energy in waves from a point source radially. ( in the beginning they thought ether existed on which the waves transferred the energy, but that is another story)
Then came the experimental discovery of nuclear energy, which emits energy radially from point sources, and is invisible to the eye . It was called radiation and the elements emitting it were called radioactive. This is where the split happens, between the strict meaning in physics of radiative transfer of energy through waves, and the nuclear community vocabulary: radiation is any ( note not particularly wave) form of radially emitted energy from a source/nucleus.
This last meaning has dominated the vocabulary of nuclear related disciplines, like health physics, and certainly the news. Certainly it is not wrong, it is just a double use of the term.
In nuclear physics you can call radiation gamma rays and be true to the wave definition, because a gamma is an electromagnetic wave that is emitted radially from the source. Alpha (helium nuclei), beta+/- ( positrons/electrons) , higher nuclear fragments from heavy nuclei breakups will also be called radiation for health physics purposes too, with the second meaning of the term.
Electromagnetic radiation has a spectrum of frequencies, beginning from infrared to gamma ray energies. At low energy, i.e. in the infrared regime, you know electromagnetic radiation as radio waves, microwaves or "heat radiation". At intermediate energies it makes up the visible light. At even higher energies, it can be ionizing, if the energy of the radiation is higher than the energy with which the electrons are bound in an atom. These range from X-Rays to gamma rays.