It's a single option in games where I see it similar to graphical presets (Low, Med, High etc) on PC. It's just named differently on consoles.
In Nioh it's Action (60FPS, lower graphics), Movie (30 FPS, best graphics) and Variable (Somewhere in between).
For FF XV it's Lite (used to be stable 30 FPS but now uncapped at variable resolutions at lower graphics) or High (30 FPS at 1080p via checker boarding with best graphics). Due to frame pacing issues (on PS4/Pro) there might be a third option in the future, not unlike Nioh, since Lite is now like Variable in Nioh. There is now no mode where you can have a steady FPS and frame pacing. It is either accept higher FPS or 30 FPS lock where both has frame pacing issues. Strangely, this is not an issue on the Xbone but it is using different processing options there.
These options should exist since people have preferences. Some people can deal with 30 FPS, some need 60 FPS, some can deal with variable FPS and/or deal with frame pacing issues. Since it's on console, it's easier (in theory, see above) to get right and not alienate demographic(s).
Edit: Seems like Horizon: Zero Dawn on the PS4 Pro will have a Performance option patch in on a later date. It's up in the air on what it means. It could be 60 FPS or it could be variable. I'm leaning on 60 FPS since Guerilla really nailed the performance at 30 FPS on both PS4 and PS4 Pro. It remains to be seen if they can pull off solid 60 FPS but if they can they might sell me on the PS4 Pro since it's a console exclusive and all.