1. Waste from extraction of uranium ores. This part is relatively insignifcant;
2. Enrichment waste. Most (all?) power-generating nuclear power plants use U235 as fuel. Mined uranium is primarily U238 with low amounts of U235. This metal needs to be enriched, which is to say the percentage of U235 needs to be made higher. This is really the only difference between reactor-grade Uranium and weapons-grade Uranium (ie the percentage of U235). These are isotopes so are chemically identical. So how do we do it? We convert it to a gas and put them through a series of centrifuges. These centrifuges will effectively increase the concentration of U235. How we do this is with Uranium Hexaflouride (UF6).
UF6 is a significant waste byproduct that requires storage. There are processes to make this less toxic (eg UF6 -> UF4) but they aren't really economic, at least not yet; and
3. The reactor fuel itself creates waste in the form of radioactive fissile products and fuel decay products. Every now and again the fuel rods need replacing. This is an expensive and highly-skilled process done by the NRC. Those byproducts need to be stored or disposed of. This article is talking about this form of waste, specifically.
Also yes many of the byproducts are more radioactive than the fuel. The stuff in the dirt tends to be comparatively stable - the unstable stuff decayed long ago. Stuff coming out of a reactor is like a year old.
https://nrcpublicblog.files.wordpress.com/2015/02/fuelrods.j...
That technician probably works with nuclear fuel every day and he's exposed to far less occupational radioactivity than a flight attendant because at higher altitudes there's less atmosphere to attenuate cosmic radiation. Even orders of magnitude more concentrated doesn't lead to some extreme amount of radiation. If it hasn't gone critical then the radiation hazard is negligible outside your body. In fact, if you were to finely grind up some Uranium and chemically process it into some biologically absorbable form and ingest a lethal amount the heavy metal poisoning would be lethal before the radioactivity.
>Also yes many of the byproducts are more radioactive than the fuel.
That's the understatement of the year. The fission products are extremely radioactive and are responsible for the massive amounts of shielding and care needed around high level nuclear waste.
>The stuff in the dirt tends to be comparatively stable - the unstable stuff decayed long ago.
Also not true, the stuff in the dirt has been constantly decaying and building up to a steady state decay chain in proportion to the half life of each isotope and the production rate of it. Fresh fuel is basically entirely Uranium with almost no decay products whereas all the radon that seeps up in basements all comes from radioactive decay of unstable isotopes underground. "The stuff in the dirt" is responsible for around 21,000 lung cancer deaths every year in the United States.
Amazing no?
Why not in reactors? Because they rely on a certain kind of subatomic process (nuclear fission) to produce energy that can only happen once in the controlled environment of a nuclear reactor.
But you idea that "being more radioactive" makes a better nuclear fuel is wrong. A good nuclear fuel is one that produces lots of energy for little input energy, is easy to mine and process, can be controlled easily, and can be disposed of safely.