The existence of ionized X-ray absorbing layers of gas along the line of sight to the nuclei of Seyfert galaxies is a well established observational fact. This material is systematically outflowing and shows a large range in parameters. However, its actual nature and dynamics are still not clear. In order to gain insights into these important issues we performed a literature search for papers reporting the parameters of the soft X-ray warm absorbers (WAs) in 35 type 1 Seyferts and compared their properties to those of the ultra-fast outflows (UFOs) detected in the same sample. The fraction of sources with WAs is >60 per cent, consistent with previous studies. The fraction of sources with UFOs is >34 per cent, >67 per cent of which also show WAs. The large dynamic range obtained when considering all the absorbers together, spanning several orders of magnitude in ionization, column, velocity and distance allows us, for the first time, to investigate general relations among them. In particular, we find significant correlations indicating that the closer the absorber is to the central black hole, the higher the ionization, column, outflow velocity and consequently the mechanical power. In all the cases, the absorbers continuously populate the whole parameter space, with the WAs and the UFOs lying always at the two ends of the distribution. These evidence strongly suggest that these absorbers, often considered of different types, could actually represent parts of a single large-scale stratified outflow observed at different locations from the black hole. The UFOs are likely launched from the inner accretion disc and the WAs at larger distances, such as the outer disc and/or torus. We argue that the observed parameters and correlations are, to date, consistent with both radiation pressure through Compton scattering and magnetohydrodynamic processes contributing to the outflow acceleration, the latter playing a major role. Most of the absorbers, especially the UFOs, show a sufficiently high mechanical power (at least approx 0.5 per cent of the bolometric luminosity) to provide a significant contribution to active galactic nuclei (AGN) feedback and thus to the evolution of the host galaxy. In this regard, we find possible evidence for the interaction of the AGN wind with the surrounding environment on large scales.