Order of Nucleophilicity
Please remember that nucleophilic substitution at a saturated carbon atom does not directly correlate with pKa. 

The pKa of a substance (in the Bronsted-Lowry definition) relates to the substance's ability to have strong interactions with $\ce{H^+}$. Thus, this interaction is mainly electrostatic in nature; since $\ce{H^+}$ is a very small, weakly polarizable ion, according to hard-soft acid base theory, strong interactions with this ion are largely electrostatic in nature, i.e. proportional to charge density.

However, nucleophilic substitution at a saturated carbon atom occurs mainly through orbital interactions, not through electrostatic interactions. Namely, the highest occupied molecular orbital (HOMO) of the nucleophile interacts with the LUMO (sigma antibonding orbital) of the substrate (usually alkyl halide). 



Since higher energy HOMOs interact better with LUMOs, molecules or ions with higher energy HOMOs are more nucleophilic.

With the specific case that you gave ($\ce{EtO-}$ and $\ce{EtS-}$), consider that sulfur is a larger atom, and the electrons in HOMO in $\ce{EtS-}$ are going to be less tighly held by nuclear charge than electrons in the HOMO in $\ce{EtO-}$. Alternatively, you can consider that the highest energy level orbital in S is 3p while that of oxygen is 2p --> electrons are more tighly held and lower in energy in $\ce{EtO-}$ --> $\ce{EtO-}$ is less nucleophilic.



Thus, if you consider the relative energy levels HOMOs in related molecules and ions, you get the general trend below:



References

Clayden, J., Greeves, N., Warren, S. Organic chemistry, 2nd ed.; Oxford University Press: New York, 2012.