The terminology is from Halmos's Lectures on Boolean Algebras.
Let $X$ be a Boolean space. A subset of $X$ is a Baire set if it an element of the $\sigma$-field generated by the clopen subsets of $X$. A Boolean space is a $\sigma$-space if the closure of every open Baire set is open; and a complete space if the closure of every open set is open.
With these definitions in mind, Halmos proves (Theorem 13, p.102) that if $X$ a Boolean $\sigma$-space, then the dual algebra $A$ of $X$ (the field of clopen subsets of $X$) is isomorphic to the quotient $B/M$, where $B$ is the $\sigma$-field of Baire subsets of $X$ and $M$ is the $\sigma$-ideal of meager Baire sets.
Since, every complete space is a $\sigma$-space, can I safely replace "$\sigma$-space" by "complete space" in the above theorem, or is there any pitfall I should pay attention to?