According to Bronsted - Lowry Concept:
An acid is a substance which can donate proton (H+):
A base is a substance which can accept a proton (H+).
All Arrhenius acids are also Bronsted acids.
But all Arrehenius bases are not Bronsted bases.
For example, NaOH is a base according to Arrhenius theory because it gives OH- ions in aqueous solution. But NaOH does not accept a proton. Thus it may not be classified as a base according to Bronsted theory.
Conjugate acids, bases
The pairs of acids and bases whihc are formed from each other by the gain of loss of a proton are called conjugate acid-base pairs.
(Topic: Ionic equilibrium, Redox reactions)