One pair that I see frequently misused in the media and in conversation is Radiation and Radioactivity.
The difference is fairly simple if you think about it physically:
Radiation is particles or energy that radiate away from a source (perhaps an explosion), usually at or near the speed of light, and can often disrupt the electrons in atoms or molecules (or sometimes even in nuclei if the radiation is high enough energy) as they get slowed down by normal matter.
Radioactivity is a condition of certain unstable atomic nuclei that will eventually give off radiation. So a cloud of Xenon 137 nuclei that escape from a burning nuclear power reactor would count as radioactivity, as would the unstable Cesium-137 nuclei/atoms they turn into a few seconds later. The electron and gamma ray that escape from the Xenon during that transition count as radiation.
- If you are in space and get struck by a Cesium-137 nuclei that was blasted from a Supernova's shock front at near the speed of light, that counts as radiation (it was radiating away from the supernova).
- If a smoker has inhaled a Polonium-210 atom, and it gets in his lungs, that atom is radioactive. The alpha particle it will eventually give off is radiation, which might cause cancer as it disrupts his biological molecules.
- Radiowaves (as all forms of light) are also radiation, even if they are too low energy to disrupt your molecules. Hence the term Cosmic Microwave Background Radiation ... which by itself can't hurt you, unless it makes the water molecules inside you vibrate.