A nuclear change involves change at the nuclear level and results in new elements (different from the reactant/s). A chemical change generates new substances, but new elements are not generated. Evidence of nuclear change is the generation of new elements, while chemical changes are observed (typically) by the generation of gases, heat, etc. (Apart from the formation of new chemical species). An example of nuclear change is the radioactivity of uranium 238. When this element undergoes radioactive decay, it transforms into thorium-234 along with generating an alpha particle. Here we see a new element being generated by transformations at the nuclear level. An example of a chemical reaction is the breakdown of glucose in the presence of oxygen, where the end product is carbon dioxide and water. Here, the result is a new chemical species (CO2 and water) but no elemental changes are there.
Hope this helps.