Answer
The principal difference is that, when the reaction occurs in anything but water, the substance doesn't act like an Arrhenius base, but it is considered a Bronsted-Lowry base.
Work Step by Step
According to Arrhenius, a base is a substance that increases the concentration of $[OH^-]$ when the reaction occurs in water.
According to Bronsted-Lowry theory, a base is a substance that can receive a proton ($H^+$) in a reaction.
