An atom can be an ion, but not all ions are atoms. There are distinct differences between an atom and an ion.
An atom is the defining structure of an element. Elemental atoms differ from each other by the number of protons in their nucleus.
For example, one way to tell oxygen atoms from nitrogen atoms would be to count the number of protons each atom has. Oxygen will have eight where nitrogen will have seven.
Stable atoms have the same number of electrons as the number of protons. These electrons form orbitals around the nucleus and cause much of the chemical properties of the element. When an atom's outermost orbital gains or loses electrons (also known as valence electrons), the atom forms an ion.
Ions are atoms or molecules that have gained or lost one or more of their valence electrons and have a net positive or negative charge.