Is Effective Nuclear Charge the same as Core Electrons?

I'm wondering, what is the difference between the two?


Using the equation for Eff: $\ce{Zeff = Z - S}$


Z being the number of protons in the nucleus and S being inner-shell electrons. 


For example: 


When calculating Lithium, I first do the electron configuration, 


$\ce{1s^2}{2s^1}$


The valence electron configuration is then 1, from looking in the periodic table - it is in the first column. Then to find the core electron configuration, I subtract the valence electron number, 1, from the number of total electrons, 3. I then wind up with 2 as my core electron configuration. Am I just doing the same equation twice if I were to calculate Zeff?


$\ce{Zeff = 3 - 2 = 1}$


They're the same thing, are they not? 


