What you are seeing here is something we tend to call an "ossia stave", which is a small staff printed over the staff in question, usually marked "ossia" (it. "or be it, alternatively"). These staves are generally aligned with the music it replaces, so you will see that each 16th note in the top small stave align with the corresponding 16th notes in the top regular staff. So your understanding is correct.
As for the why: Aaron did already point out that this case is for pianos with sufficient range. But generally you will find such ossia passages for many different reasons, such as
- Different instrument ranges
- Different technical skill required
- Preference (a composer might offer alternative ways to play something as you seem fit)
These things might also come from the editor, e.g. because the editors thinks "this passage can be done differently on a modern instrument", or "I like this passage better this way", or even "we have different sources, and one does it like that".
Unless your are insanely skilled it should be impossible to play these passages at the same time, and you are not expected to do so. Nevertheless considering that Liszt did like improvise, adapt, arrange and change you may try to find a compromise between these options if you really want to.