Redshift surveys provide a possibility for three-dimensional analysis of the matter distribution. But this problem is complicated by the fact, that observed redshifts of extragalactic objects (which are almost the only one source of information about the distance) are not ``pure'' cosmological redshifts (caused by expansion of the Universe), but are contaminated by gravitationally-induced peculiar velocities of the objects. The distances calculated from the observed redshifts are called distances in redshift space in contrast to real space.
Speaking about the clustering analysis in redshift space one usually resolves the redshift-space, $s$, or real-space, $r$, separation between two objects into two components, $\sigma$ and $\pi$, where $\sigma$ is a projection onto the line-of-sight, and $\pi$ is a projection onto the plane perpendicular to the line-of-sight. Sometimes these projections are called transverse and parallel separations correspondingly. It is assumed that only parallel separation $\pi$ is contaminated by the peculiar velocities, thus the redshift-space and real-space distances are defined as where $\pi \neq \pi '$ due to peculiar velocities.