It can be a bit confusing, yeah.
Basically, the 3DS has had three games released in Japan:
- Senran Kagura
- Senran Kagura Burst
- Senran Kagura 2
Senran Kagura Burst is less of a sequel, though, and more of an expanded remake, containing the entirety of Senran Kagura but doubling the length of the game by adding a whole new campaign. That's the one we released.
Senran Kagura 2 takes place IMMEDIATELY after the events of Senran Kagura Burst.
Then there are the Vita games:
- Senran Kagura Shinovi Versus
- Senran Kagura Estival Versus
These games take place even farther in the future -- so timeline-wise, Shinovi Versus takes place well after the events of Senran Kagura 2, and sort of begins a new story altogether.
The idea, I believe, is to have the 3DS games tell one complete story arc, and the Vita games tell another. You can think of them kind of like two series running concurrently... though Shinovi Versus does directly reference the events of Senran Kagura Burst (while ignoring the events of Senran Kagura 2, since SK2 didn't exist yet when Shinovi Versus was being developed).
Yes, Shinovi Versus is definitively compatible with PSTV.
-Tom