Isotopes are defined as:

Isotopes are specifically defined as atoms of the same element that have the same number of protons but different numbers of neutrons. This distinction leads to variations in their mass while retaining the same chemical properties because they have identical electron configurations.

The significance of this definition lies in the fact that the number of protons defines the element, while the different neutron counts lead to variations in atomic mass, allowing us to distinguish between isotopes of the same element. For instance, carbon-12 and carbon-14 are both carbon isotopes, differing only in the number of neutrons—six in carbon-12 and eight in carbon-14.

In contrast, options that suggest different numbers of protons lead to identifying different elements altogether, which does not apply to isotopic definitions. Additionally, describing different elements with various properties does not accurately capture the essence of isotopes, as it strays from the focus on variations of a specific element's neutrons. Thus, the understanding of isotopes hinges on the relationship of neutrons to protons within the same elemental category.