We know that isodiaphers have same difference in neutrons and protons, but I encountered another definition:
Atoms which have same isotopic axis are called isodiaphers.
I don't know what it means by "isotopic axis". Please try to explain in simple words.
These are basic terms of radiochemistry:
Isotopes are nuclides with a common number of protons $Z$.
Isobars are nuclides with a common number of nucleons $A$.
Isotones are nuclides with a common number of neutrons $N$.
Isodiaphers are nuclides with a common neutron excess $N-Z=A-2Z$.
Thus, in the chart of the nuclides, isodiaphers are found in diagonals from bottom left to top right. For example, the mother and daughter nuclides of alpha decay are isodiaphers.