A bounded distributive lattice L has two unital semilattice reducts, denoted L̂^ and Lv. These ordered structures have a common canonical extension Lδ. As algebras, they also possess profinite completions, L̂, L̂^ and L̂v; the first of these is well known to coincide with Lδ. Depending on the structure of L, these three completions may coincide or may be di erent. Necessary and sufficient conditions are obtained for the canonical extension of L to coincide with the profinite completion of one...