What is the difference between Boolean Algebra and Boolean Lattice?
According to Wikipedia, these are two names for the same concept. You can differentiate them by stating that Boolean algebra is an algebraic structure having operations $\land,\lor,\lnot$ satisfying certain axioms, and in contrast a Boolean lattice is a lattice having certain properties; but the two definitions are equivalent. Sometimes Boolean algebra and Boolean lattice refer to specific constructions (subsets of a set), but according to Stone's representation theorem these two definitions are also equivalent.