Difference between 18 electron rule and effective atomic number rule
Both of these rules are equivalent and are related to transition metals attaining a noble gas configuration of electrons in coordination complexes. The difference between them is the number of electrons given to the central metal. 

The effective atomic number uses all of the metals electrons. For example, in an $Fe^{2+}$ complex, the central iron atom has 24 electrons, and you would want the ligands coordinated to the metal to contribute another 12 electrons to reach 36 electrons, the next noble gas configuration. 

The 18-electron rule is a simplification of the EAN. There is always a noble gas configuration of electrons for the metals core orbitals (e.g. 1s2s2p3s3p for $Fe^{2+}$), so you can ignore these electrons in the counting scheme. For transition metals, this means that the only important orbitals are the valence nd(n+1)s(n+1)p orbitals, which can hold a total of 18 electrons. For $Fe^{2+}$, there are 6 electrons in these orbitals. Again, the ligands would need to donate 12 electrons to reach the 18 electron limit.