Context. Nowadays, we know that the origin of the cosmic X-ray background (CXB) is mainly due to the integrated emission of active galactic nuclei. Therefore, in order to obtain a precise estimate of the contribution of different source classes to the CXB, it is crucial to achieve full characterization of the hard-X ray sky. Aims. We present a multifrequency analysis of all sources listed in the third release of the Palermo Swift-BAT hard X-ray catalog (3PBC) with the goal of (i) identifying and classifying the largest number of sources adopting multifrequency criteria, with particular emphasis on extragalactic populations and (ii) extracting sources belonging to the class of Seyfert galaxies to present here the release of the second version of the Turin-SyCAT. Methods. We outline a classification scheme based on radio, infrared (IR), and optical criteria that allows us to distinguish between unidentified and unclassified hard X-ray sources, as well as to classify those sources belonging to the Galactic and the extragalactic populations. Results. Our revised version of the 3PBC lists 1176 classified, 820 extragalactic, and 356 Galactic sources, as well as 199 unclassified and 218 unidentified sources. According to our analysis, the hard X-ray sky is mainly populated by Seyfert galaxies and blazars. For the blazar population, we report trends between the hard X-ray and the gamma-ray emissions based on the fact that a large fraction of them also have a counterpart detected by the Fermi satellite. These trends are all in agreement with the expectations of inverse Compton models which are widely adopted to explain the blazar broadband emission. For the Seyfert galaxies, we present the second version of the Turin-SyCAT, including a total of 633 Seyfert galaxies, with 282 new sources corresponding to an increase of ~80% with respect to the previous release. Comparing the hard X-ray and the infrared emissions of Seyfert galaxies, we confirm that there is no clear difference between the flux distribution of the infrared-to-hard X-ray flux ratio of Seyfert galaxies Type 1 and Type 2. However, there is a significant trend between the mid-IR flux and hard X-ray flux, confirming previous statistical results in the literature. Conclusions. We provide two catalog tables. The first is the revised version of the 3PBC catalog based on our multifrequency analyses. The second catalog table is a release of the second version of the Turin-SyCAT catalog. Finally, we highlight that extensive soft X-ray data are already available in the form of the Swift archive which can be used to search for potential counterparts of unidentified hard X-ray sources. All these datasets will be reduced and analyzed in a forthcoming analysis to determine the precise position of low-energy counterparts in the 0.5–10 keV energy range for 3PBC sources that can be targets of future optical spectroscopic campaigns; this is necessary to obtain their precise classification.