What do we call nuclei of the same element that have different masses?

An element is defined by #"Z, the atomic number"#, which specifies the number of positively charged, massive particles present in that element's nucleus.....

#Z=1, "the element is hydrogen"#; #Z=2, "the element is helium"#; #Z=3, "the element is lithium"#;...#Z=33, "the element is arsenic"#.

Because elements are to a first approximation electrically neutral, #Z# thus also defines the number of electrons, particles of negligible mass that are conceived to whizz about the nuclear core. Loss and gain of electrons between elements, and the bonding between elements, when electrons are shared between them, underlies and explains ALL of chemistry.

Within the nucleus, a given element has a SPECIFIED number of protons, but a VARIABLE number of neutrons, massive particles of ZERO electric charge, and this gives rise to the phenomenon of isotopes. And this is best illustrated by an example.

All hydrogen nuclei have #Z=1#, i.e. they have the ONE, positively charged particle in their nucleus. A smaller percentage of hydrogen atoms also have 1 neutron in the nucleus to give the #"deuterium isotope"#, #""^2H#, and a smaller percentage of hydrogen atoms have 2 neutrons in their nuclei, to give the #"tritium isotope"#, #""^3H#.

The atomic mass quoted on the Periodic Table, is the weighted average of the masses of the isotopes. As atoms become heavier, they tend to exhibit greater isotopic variation, and again the quoted atomic mass is the envelope of the isotopic masses.