Before I delve into that answer, let me basically define what a base and an alkali, are.
A base is, very simply, a substance which reacts with an acid, to form a salt and water.
Acid + Base --> Salt + Water
An alkali would, very simply, mean a water-soluble base, something which gives OH-(hydroxyl) ions when it dissolves in water.
Cu(OH)2 --> Cu2+ + 2OH-
Clearly, all hydroxides like this one, Cu(OH)2 (Copper Hydroxide), is a alkali, and a base as well, because it reacts with an acid, to form salt and water.
Cu(OH)2 + 2HCl --> CuCl2 + 2H2O.
The thing is that bases which are oxides such as Copper(II) Oxide CuO, are not water soluble, and thus don't give hydroxyl ions when dissolving in water - they don't dissolve in water.
CuO + 2HCl --> CuCl2 + H2O.
CuO -->(No OH- ions).
THUS, in conclusion, all alkalis are bases, but all bases (except hydroxides) are NOT alkalis.