Answer
The Brnsted-Lowry definition, being less specific, is more encompassing than the Arrhenius definition.
Here's what I mean.
The Brnsted-Lowry definition says that:
An acid donates a proton (H+) No further qualification is involved.A base accepts a proton(H+)No further qualification is involved.The Arrhenius definition says that:
An acid donates a proton (H+)with the qualification that it occurs upon dissociation and the proton is donated to water.A base donates an OH−with the qualification that it occurs upon dissociation and the OH−is donated to water.As a result of the more specific nature of the Arrhenius definition, it is confined to only aqueous solutions. With Arrhenius bases, it is additionally specific in that a OH must be donated to solution... while protons aren't really considered.
One example of a Brnsted-Lowry base that is NOT an Arrhenius base is sodium ethoxid
We should notice that it can accept a proton (by donating electrons), just like the Brnsted-Lowry base definition requires, but it does not donate an OH to water; it can't, because we aren't even using water as the solvent!
Thus, sodium ethoxide in ethanol is not an Arrhenius base; though, it IS a Lewis base since its oxygen donates two valence electrons to get its proton.