In Borel/Ji " compactifications of symmetric and locally symmetric spaces " the Baily Borel compactification of a locally symmetric space is defined as $$\Pi\backslash(X\coprod_{\bf{P}}X_{P,h})$$ where $\Pi$ is an arithmetic group,$X=G/K$ with $G$ the real locus of an algebraic group $\bf{G}$, $K$ a maximal compact subgroup, $\bf{P}$ a maximal parabolic subgroup of $\bf{G}$ and $P$ it's real locus. Moreover, $X_{P,h}$ refers to the hermitian part of the boundary symmetric space associated to $P$.
Now, I have seen people use the hermitian parts $X_{\bf{P},h}$ of the maximal parabolic subgroups $\bf{P}$ as boundary component. Doesn't this make a difference? In general the two boundary spaces $X_P$ and $X_\bf{P}$ are different. Thanks!
Edit: The boundary spaces differ by a Euclidean factor. My guess is that the hermitian part of the boundary spaces are equal.