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In these reactions between alkyl halide and KOH in different states the product is different only because of the change in state of KOH from aqueous and alcohol .

Can someone explain the mechanism which causes this drastic change?

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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: enter image description here

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