• Isotopes are atoms of the same element with different numbers of neutrons.(Aren't elements)
• The presence of isotopes in different amounts , in the same elements , results in different physical properties between the identical elements due to the difference in the relative atomic mass of the two identical elements ?
bullet 1: isotopes
are the same element
bullet 2: Yes, the difference in physical properties is caused by the different numbers of neutrons (which in turn affects relative mass). For example, carbon-14 is less stable than its isotope carbon-12, and hence radioactive. This difference forms the basis of carbon dating.
If you have just one atom of each isotope, you can say that the atoms have different physical properties. In this example, carbon-14 is radioactive, whereas carbon-12 is not.
As you point out, two pieces of carbon could have different proportions of each of the carbon isotopes. So in that sense, we can say that the pieces of carbon have different physical properties, but most of those differences operate at the atomic level. For example, if one piece did contain carbon-14, but the other did not, we could say that only the carbon-14-containing piece was radioactive, but that radioactivity will operate at the atomic level, that is, individual atoms will undergo radioactive decay.