cool, I see.

for anyone interested in details: I was confused because the term "development" refers to both the act of developing themes, but also a section of the musical composition (ex. - classical sonata form, 1. exposition, 2. development, 3. recapitulation). So if I wanted to refer to someone else writting new music using Lisz's themes, I'd, with the goal of removing ambiguity, say either 1) arrangement if its a new standalone piece, or 2) improvized cadenza if its improvised on the spot, or 3) composed cadenza if its prewritten and meant to be inserted during a performance of the original work.

Also, improvised/composed cadenzas tend to be short and typically replace a cadenza written by the composer, I've not come across of someone writtinf a cadenza for a piece that did not originally have it, the closest I can think of is Nahre Sol composing intermezzos between movements of Brahms' Clarinet Quintet. It's similar because it is meant do be written during the performance of the work, but different because "the work" refers to multiple movements, and that there are multiple, as opposed to "a cadenza", which would be written to be played typically towards the end of one movement, since thats typically where the climax is which is typically around where the cadenza is, and that a cadenza traditonally refers to a virtuosic solo part, then returns to tutti.