Isotopes are atoms of the same element that have different numbers of neutrons in the nucleus. Remember that it is only the number of protons that determines the identity of an element.
Let's look at the simplest element, hydrogen. The common variety of hydrogen has a single proton in the nucleus and a single electron in an orbital surrounding the nucleus.
There is another variety of hydrogen that has a neutron in the nucleus as well as the proton. It still has only 1 proton so it remains the element hydrogen but now it weighs twice as much. This is an example of an isotope and this isotope of hydrogen is called deuterium. When it is combined with oxygen in the compound water; that water is called heavy water because indeed it is heavier than ordinary water. We call deuterium a stable isotope.
There is still another isotope of hydrogen, called tritium, that has 1 proton and 2 neutrons in the nucleus.
Tritium, unlike deuterium, is unstable and tends to spontaneously decay by emitting a high energy electron from one of the neutrons in the nucleus. When this happens; the neutron is changed into a proton and a new element is formed. This is an example of a nuclear reaction...in this case, beta decay. Tritium is a radioisotope.
The new element that is formed has 2 protons and 1 neutron in the nucleus and is an isotope of helium. The common variety of helium differs from this isotope in that it has 2 protons and 2 neutrons in the nucleus for a mass of 4 amu.