The obvious difference, described in more detail at the link below, is the different number of neutrons in the isotope that make it different from the original element.
A great example are the various isotopes of uranium, some of them useful for just about nothing except to be mildly radioactive, some of the useful to act as fuel in nuclear reactors, and some of them useful as the core of a warhead in a nuclear reactor. Amazing what different isotopes can mean for the various applications, etc.
Again, the link below gives quite a bit more detail about what isotopes are and can be used for, etc.
The atom is made up of three major particles. Protons and neutrons which make up the nucleus and electrons which surround the nucleus. It is the number of protons, or the atomic number, the one that makes an element what it is. If you change the number of protons, you no longer have that element. The other nuclear particle is the neutron. The mass number is a sum of the number of protons, or atomic number, and the number of neutrons. It is these particles which give an atom its mass, the electrons do not weigh much and their contribution to the mass is negligible. If you change the number of neutrons, the mass number (which is a sum of protons and neutrons) changes, but the atomic number remains the same. This is how you can determine if an atom is an isoptope of the same element. The mass number is different, but the atomic number is the same.
Example: Hydrogen has 3 isotopes: Protium: atomic number=1, mass number= 1; Deuterium: atomic number= 1, mass number= 2; and Tritium: atomic number=1, mass number = 3.