They are isomorphic in the strong sense that their logical interpretations are identical. Applying Curry-Howard, a function type is an implication, so a curried function with type A -> B -> C is equivalent to an implication that says "If A, then if B, then C." Likewise, a tuple is a conjunction, so a non-curried function with type (A, B) -> C is equivalent to the logic statement (A /\ B) -> C, i.e., "If A and B then C." Both logical statements are equivalent, i.e., have the same truth tables.

However, as the article outlines, there are differences (both positive and negative) to using functions with these types. Curried functions allow for partial application, leading to elegant definitions, e.g., in Haskell, we can define a function that sums over lists as sum = foldl (+) 0 where we leave out foldl's final list argument, giving us a function expecting a list that performs the behavior we expect. However, this style of programming can lead to weird games and unweildy code because of the positional nature of curried functions, e.g., having to use function combinators such as Haskell's flip function (with type (A -> B -> C) -> B -> A -> C) to juggle arguments you do not want to fill to the end of the parameter list.

That's a fair point, they are all isomorphic.

The distinction is mostly semantic so you could say they are the same. But I thought it makes sense to emphasize that the former is a feature of function types, and the latter is still technically single-parameter.

I suppose one real difference is that you cannot feed a tuple into a parameter list function. Like:

fn do_something(name: &str, age: u32) { ... }

let person = ("Alice", 40);

do_something(person); // doesn't compile

Probably just that having parameter-lists as a specific special feature makes them distinct from tuple types. So you may end up with packing/unpacking features to convert between them, and a function being generic over its number of parameters is distinct from it being generic over its input types. On the other hand you can more easily do stuff like named args or default values.

The parameter list forces the individual arguments to be visible at the call site. You cannot separate the packaging of the argument list from invoking the function (barring special syntactic or library support by the language). It also affects how singleton tuples behave in your language.

The article is about programmer ergonomics of a language. Two languages can have substantially different ergonomics even when there is a straightforward mapping between the two.

It's not that they are meaningfully different. It's just acknowledging if you really want currying, you can say 'why not just use a single parameter of tuple type'.

Then there's an implication of 'sure, but that doesn't actually help much if it's not standar' and then it's not addressed further.

The tuple style can't be curried (in Haskell).

Presumably creating a different class for parameter lists allows you to extend it with operations that aren't natural to tuples, like named arguments.