A nuclear reaction involves changes to the nucleus of an atom. Reactions can be spontaneous or can result from the interaction with other particles.
A spontaneous nuclear reaction may result in the release of a neutron or proton from the nucleus. Sometimes the nucleus can release several of these at once. Sometimes they can split into two nuclei. An "alpha particle" is the result of the release of two protons and two neutrons together. You should recognize that this configuration forms the nucleus of a Helium atom.
If a nucleus collides with another particle, there can also be a reaction. Neutrons can cause reactions. Such an interaction could simply result in the Neutron being absorbed. This creates a new isotope of the element. Neutron absorption can make a nucleus unstable and more likely to split into several parts.
Chemical reactions , on the other hand, do not change the nucleus of the atoms. These reactions involve only the bonds between atoms and the clouds of electrons which surround the nucleus.
If you set fire to a piece of paper, oxygen from the air is combining with carbon and hydrogen in the paper to form carbon dioxide, carbon monoxide, water, and a few other compounds. If you could capture all of the smoke and measure all of the paper and oxygen consumed in the process, you would find that you start with the same atoms you end up with.
A chemical reaction which begins with a certain amount of carbon, nitrogen, and zinc will have those same elements in the same quantities at the end of the reaction. A nuclear reaction may start with a certain quantity of plutonium and end with some amount plutonium, uranium, lead, and iron (and probably lots of other things).