When concentrated forms of radioactivity find themselves in the environment, or any accessible areas to people, this is known as radioactive contamination. The radioactivity has to have been concentrated before this can really be considered as such because technically all things are radioactive. In this sense, calling your scratch paper or food scraps radioactive waste might scientifically be correct but by convention and current definition, the radioactivity has to be concentrated in waste materials before they require legal classification as such or handling and unique disposal controls.
Natural uranium and radium in rocks do not require special controls when those rocks are granite counter tops in your home which emit radon along with an array of gamma and beta radiation. If the radioactive elements were extracted from the granite (or any other ore), then this concentration receives a special classification known as NORM which stands for naturally occurring radioactive materials. Similarly biproduct material generated by separating out only one of many radionuclides in an ore can generate NORM. This is the case in areas where uranium mining and milling have occurred because when the uranium is removed, all the radioactive decay products (of the uranium) are left behind. These radioactive decay products are again classified as NORM and include radionuclides such as radium and thorium (along with their radioactive decay products).
At environmental levels, these and other radionuclides are not considered harmful in that life was designed to coexist with radioactivity (given that all things have technically always been radioactive). Concentrating radioactivity can generate hazards of course. Just as concentrating heat, pressure or electricity can be truly lethal, even concentrating NORM can create radiological hazards. Naturally occurring radium for example when accumulated into less than a single gram (less than 4% of an ounce) of pure radium metal will generate a radiation area which at any nuclear facility would require multiple controls including access restrictions, training and use of procedures for handling the material. A full gram of radium is actually a defining unit in nuclear science in that it contains exactly 1 Curie of radioactivity (named after the famous Nobel laureate Marie Curie). A single Curie is generally considered a large amount of radioactivity in a gram of material as it is many trillions of times more concentrated than most naturally occurring environmental levels (even though the radium is naturally occurring, it is not naturally found at such a high concentration).
When concentrated amounts of radioactivity find their way into the environment, this is considered environmental contamination. This can occur at many different levels, higher concentrations such as those created by Chernobyl or lower levels such as those which occurred at Fukushima are examples. In the United States, radioactive contamination is evaluated based on both the chemical form of the radioactivity and the particular isotopes present. The chemical form can range from being a liquid, gas, metal, or even a water soluble salt or an insoluble ceramic. This chemistry of the radioactivity determines how it will interact and move in both the environment and inside the body (if it makes it there). The isotopes present determines what kind of radiation the radioactivity will emit such as gamma, beta or alpha radiation. All of these features are important in assessing the potential hazards associated with environmental contamination. If the radioactivity is in a salt, it can move through the food chain similar to table salt making it both mobile in water and easily incorporated into crops. Depending on the isotopes present, the types of radiation emitted will determine the amount of hazard present for both external exposure to the contamination as well as the hazards associated with any form of ingestion of the radioactivity. The US Environmental Protection Agency has set protective action guidelines for emergency response actions following any accidental environmental release of radioactivity. Similarly the US Food and Drug Administration has well defined derived intervention levels for use in recommending actions taken regarding radiologically contaminated land. These recommendations involve such things as embargo or limited use for any food products which might be derived from that land. This depends on the type of food which would be brought to the market along with the chemical form, concentration and type of radioactivity present. Generally these kinds of questions will compare the effects to those readily available in the environment. Just as the amounts of heat, sound and electricity you can encounter readily in the environment are typically considered safe, so also the radioactivity and radiation levels found in the environment and naturally occurring in our food is considered safe. A good example of this is the minimum content of potassium you absolutely have to have in your body just to live. Given that you will die without potassium and that potassium is itself fairly radioactive, this in a sense defines a safe exposure to internal radioactivity and radiation if for no other reason than that you will die without it.