[btschaegg]

Okay, I'll have a go:

State is the data required to continue the operation of a program. That's always the case (also in non-FP contexts), but state is often smeared all over a program as only loosely and implicitly connected pieces whereas FP is mainly concerned with how to manage state (and thus also with how to compose such pieces of state into a greater whole so it's easier to manage).

Edit: Note that there is also "data you don't need for continuing the operation of the program", which we could categorize as "input", "output" and "wasted memory/storage/cpu cycles". The last of the three can obviously still be crucial for other reasons than program execution (e.g. debugging), which makes the line between output and waste blurry.

[RangerScience]

I like it! I don't know if I agree, but, the category of "data required to continue the operation of the program" is a pretty excellent category, thank you for pointing it out!

Maybe... As you say, state is the information required for continued execution. Which would make "data" the information that's carried through the program. Like - parts of an HTTP request are "state" because they're what you use to route the packet through the internet. The other parts are "data", because all the intermediate programs don't use it during their operation; it's just passed through.