Exactly.
The most common ELI5 definition of functional programming I get from other developers is that you're piping multiple statements together into a single chain of processing [input(s) > multiple levels of processing > output(s)], without having to explicitly declare variables to hold the temporary inputs and outputs between each sub-statement within the chain. I know just enough to understand that this isn't the "proper definition", but that workflow is true enough that it's what many people associate functional programming with.
The problem with that particular definition is that it tries to make the primary benefit of functional languages seem to be this piping/chaining mechanism. Yet these languages are still written procedurally, executing multiple such pipes in sequence. You still have variables holding the inputs and outputs of each chain, so you can pass them to other unrelated chains. It reduces the overall number of statements and the manual variable/memory management required, but each statement is simply a compressed version of multiple statements merged into one, enforcing "fake immutable" variables for the inputs/outputs within the chain. You don't really have "immutability"; you simply have automatic variable management between sub-statements in a chain.
Now, show me a functional language where the entire program is written as a single piped chain, and I would classify that as its own genre. Literally, the entire program would have to be written top-down as a single block of code that chains every single required input from the top-level, all the way down to a single output, without using a single explicitly declared variable. Only the first line of code would be unindented at the first column, with all other lines having to be indented as part of that primary block. Now that would satisfy me as being "unique" or "different than procedural".
What is the primary metric of a functional language? Is it to write write golf code[1] that folds 10 "procedural statements" into a single 3-line "functional block"? To me that's not "functional programming"; that's just writing less code by chaining multiple operations into smaller blocks, reducing the complexity of having to explicitly declare more global or widely scoped variables.
Random thought association: is perl's well-known Schwartzian transform (@sorted = map { ... } sort { ... } map { ... } @unsorted), applied as a concept to an entire language, what makes a "functional language"? To me, that doesn't seem like enough of a scope change to warrant a different language "type".