A quick way to remember these three families is to ask which of the three numbers \(Z\) (protons), \(A\) (mass number) or \(N\) (neutrons) is being held fixed.
Step 1: Fix the protons then isotopes.
If two nuclei share the same number of protons \(Z\), they are the same element; only their neutron count (and hence \(A\)) changes. These are isotopes. For carbon, \(^{12}_{6}C\) and \(^{14}_{6}C\) both have \(Z=6\), so they are isotopes.
Step 2: Fix the mass number then isobars.
If instead the total nucleon count \(A\) is the same while \(Z\) differs, the nuclei weigh alike but are chemically different elements. These are isobars. For \(A=40\), \(^{40}_{18}Ar\) and \(^{40}_{20}Ca\) are isobars.
Step 3: Fix the neutrons then isotones.
If the neutron number \(N=A-Z\) is the same while both \(Z\) and \(A\) differ, the nuclei are isotones. Silicon \(^{30}_{14}Si\) (\(N=16\)) and phosphorus \(^{31}_{15}P\) (\(N=16\)) are isotones.
Step 4: One-line contrast.
Isotopes match in protons, isobars match in total mass number, and isotones match in neutrons.
\[\boxed{Z\text{ same} \Rightarrow \text{isotopes};\ A\text{ same} \Rightarrow \text{isobars};\ N\text{ same} \Rightarrow \text{isotones}}\]