True overall (regarding overall alpha emitter load), the issue with fallout is radioactive Iodine, Stronium, Cesium, etc. Those elements have short half lives and won't be as present in significant quantities in flue emissions because of the age of coal (just as daughter products in much lower concentrations than the Uranium). Notably, they're also present in 'hot' reactor fuel, albeit in different ratios/qtys (usually) than fallout.
Notably, Stronium-90 levels in deciduous teeth of kids born in the 80's.
"Strontium-90 concentrations in deciduous (baby) teeth of 515 children born mainly after the end of worldwide atmospheric nuclear bomb tests in 1980 are found to equal the concentrations in children born during atmospheric tests in the late 1950s. Recent Sr-90 concentrations in the New York-New Jersey-Long Island metropolitan area have exceeded the expected downward trend seen in both baby teeth and adult bone after the 1963 ban on atmospheric testing. Sharp rises and declines are also seen in Miami, Florida. In Suffolk County, Long Island, Sr-90 concentrations in baby teeth were significantly correlated with cancer incidence for children 0 to 4 years of age. "
Stronium in teeth is a proxy for Stronium in bones too, and those don't fall out.
