yes, "clear nylon" and "fluorocarbon" are totaly different materials, even if they are both plastic "nylon".
fluorocarbon has more density, so strings made of this material are thin but tight, and they sound brighter, clearer and with long sustain.
clear nylon is less dense, so strings made of this material are large but loose, they sound mellower and with shorter sustain. the clear nylon sound is the classical sound you hear from old recordings, after the advent of nylon strings over the gut.
here are a couple examples:
this is a soprano tuned in D:
https://www.youtube.com/watch?v=H865uHF3WLg
this is a tenor (I think it's actually a concert with a big body):
https://youtu.be/K-8JCFDtEYE?t=98
fluorocarbon is rather recent, and it was "discovered" as a material for strings in the past few years. it's not produced by string companies, but it's produced by fishing companies, because it's the material used for fishing leaders (if you search on youtube and on the web, you'll find in depth topics about Seagur fishing leaders): it came out that with thinner strings there were a good amount of tension, plus a bright and modern tone, so guitarists and other stringed-musician started using them.
different brands made a selection of gauges and tensions, to create the sets we buy, and the differences are few: for example, the Worth Medium set is identical to the D'Addario EJ99 set, except for the C, which is bigger in the D'Addario set.
Martin M600 have smaller G, E and A, but an even bigger C than D'Addario's.
some users decided to buy bulk fishing leaders instead of buying sets of strings.
so, for a modern, bright clear and sustained sound, fluorocarbon is the best choice, bot for some users it's just too bright.
I like it, but I also like the short-sustained mellow tone of nylon strings, for a different purpose.
for example, Jake Shimabukuro uses D'Addario clear nylons:
https://www.youtube.com/watch?v=PB3RbO7updc
with his style of playing, I think that fluorocarbon could be too harsh and thin:
https://www.youtube.com/watch?v=ABf5Z84nQAo
https://www.youtube.com/watch?v=q0IFWSvMwc8
these two are the D'Addario EJ99T, for example.