Two atoms are considered to be of the same element if they have the same number of protons in their nuclei. The number of protons is what determines the atomic number (Z) of an element. Therefore, if two atoms have the same atomic number, they belong to the same element.
For example, if two atoms have 6 protons in their nuclei, they are both carbon atoms, regardless of any other properties or differences they may have, such as different numbers of neutrons or different charge states. The atomic number uniquely identifies an element and determines its chemical properties.