Ionizing radiation

Ionizing radiation is the term given to forms of radiation that are energetic enough to displace orbiting electrons from the atoms in the absorbing medium, thus forming positive ions. 

Forms of ionizing radiation

Indirect

Indirect ionizing radiation involves uncharged particles. X-rays and gamma radiation are the commonest forms of indirect ionizing radiation. Occasionally ultraviolet rays are energetic enough to cause ionization. Most of the ionization associated with electromagnetic radiation is indirect via secondary electrons created secondarily to the primary electrons, which are formed by the initial Compton and photoelectric effects. 

Neutrons may also indirectly ionize via their interactions with hydrogen nuclei.

Direct

Direct ionizing radiation involves charged particles. Alpha and beta particles from radioactive decay are examples of direct ionizing radiation.

Indeed any atom or subatomic particle with enough kinetic energy can be ionizing e.g. positrons.

Non-ionizing radiation

Most of the electromagnetic spectrum is non-ionizing, i.e. majority of the ultraviolet wavelengths, visible light, infrared, microwaves and radio waves. Sound waves are also of too low energy to ionize. Therefore both MRI and ultrasonography use non-ionizing radiation.