Gamma spectrum analysis with simple equipment can differentiate fallout from weapons vs. reactors; tell if the fission was via uranium or by plutonium; tell the relative age of the sample; determine certain environmental conditions at the time of release.
Remnants of nuclear events leave different traces, some uniqueTrinitite has Cs-137, Sr-90 but also types of radioactive europium, a prompt activation product, formed at Trinity in the soil by the moderating action of rainwater from a very recent storm (said storm that actually delayed the shot). Plutonium and Pu byproducts are present.
Chernobyl contaminated vegetation is presently showing only Cs-137, as any Cs-134 is long decayed away. Furthermore Vegetable contamination is primarily Cs due to the preferential biological disposition of elemental cesium in plants. Closer to the NPP, solid debris can be found, including fuel fleas (tiny pieces of actual nuclear fuel)
Fukushima contaminated samples are showing both Cs-134 and Cs-137. In time only the Cs-137 will remain.