I believe it is more accurate to refer to an isotope as a particular form of an element.
An element is defined by the number of protons in a nucleus. The atomic weight of an element is the geometric average of the weights of all isotopes of the element (geometric because it is weighted by their relative abundance.) Deuterium is called deuterium because each atom has a neutron in addition to the proton. It is the same element with a different atomic weight (tritium is hydrogen with 2 neutrons). If you look at a periodic table of the elements, the atomic weight of hydrogen is 1.008, 1 for the proton and .008 for the extra neutrons in deuterium and tritium which are naturally occurring.