Presently there are four "universes" in the franchise.
The classic series, consisting of I-IV (and the various side games and multimedia from the era), and taking place in Algol
PSO1/PSZero, though their connection is fairly loose. Also worth noting that while the final form of PSO1 did not have any direct connection to the classic series, it was at one point planned to link with PSIII.
PSU/Portable series, dealing with SEED and the Gurhal System
And the Oracle universe, consisting of PSO2, PSO2es (mobile companion game, currently JP exclusive), PS Nova (JP Vita spin-off), and IDOLA (JP mobile spin-off)
These four universes each have their own setting, characters, lore, continuity, and gameplay style, but are tied together by similar plots and themes, some musical motifs, general terminology, the Science Fantasy aesthetic, and being excellent games.
That said, if you're willing to bend canon a bit, it's not difficult to read between the lines and draw connections unifying the multiverse. Especially since PSO2 has a few instances of transdimensional travel within the Oracle continuity.