What is the difference in (alc) and (aq) states in reaction mechanism?
Nucleophilic substitution always competes with Elimination reaction in such cases.

What is the difference between them?

As put there by philipp:


  In alcoholic solution the $\ce{KOH}$ is basic enough ($\mathrm{pK}_{\mathrm{a}}$ 15.74) to deprotonate a small amount of alcohol molecules ($\mathrm{pK}_{\mathrm{a}}$ 16–17)), thus forming alcohlate salts $\ce{ROK}$. The alcoholate anions $\ce{RO-}$ are not only more basic than pure $\ce{OH-}$ but they are also bulkier (how much bulkier depends on the group $R$). The higher bulkiness makes $\ce{RO-}$ a worse nucleophile than $\ce{OH-}$ and the higher basicity makes it better at $\mathrm{E}2$ eliminations.


Mechanisms below: