Atomic Number
The total number of unit positive charges present in the nucleus of an atom is known as its Atomic Number which is equal to the number of protons in the nucleus of an atom. Atomic Number for any two different atoms is never same and hence can be used to distinguish two different atoms.
Mass Number
It is the sum of neutrons and protons of an atom present in nucleus. Mass Number for two different atoms can be same. The Atomic Mass of an atom is approximately equal to its Mass Number as mass of a neutron as well of a proton is one unit on atomic mass scale.
