Comparator.comparing expects a Function which describes a comparable property of the elements. So String::length is sufficient as length() is a property of the String evaluating a String to an int (that’s why comparingInt is preferable here).

In contrast, String.compareToIgnoreCase and String.compareTo are comparison methods. They compare two String objects. So references to them are sufficient where a Comparator is expected, but not where a property Function is expected.

It’s like you have a factory saying “Gimme an engine, and we build a car for you” and you are trying to give them a complete car. While that existing car is valid where a car is expected, there is no sense in passing it to the factory to built a car.

Unfortunately, the current compiler implementation is very bad at reporting error with functional signatures. You will almost always see messages like “Cannot make a static reference to the non-static method …” when signatures mismatch.

The sort method expected a Comparator.

When you do this, you are indeed providing one.

 listDevs.sort(Comparator.comparing(String::length));

Same happens here(but a bit non-intuitive):

 listDevs.sort(String::compareToIgnoreCase)
 listDevs.sort((left, right) -> left.compareToIgnoreCase(right)); // same thing as above

That's exactly the definition of a Comparator - take two Strings and return an int.

The line that you say how come this works: listDevs.sort(Comparator.comparing(String::length)); is actually pretty simple.

Comparator.comparing takes a Function that transforms your input type into something that is Comparable. In your case takes a String and returns an Integer; which is Comparable.

JLS says Compile-Time Declaration of a Method Reference of ReferenceType :: [TypeArguments] Identifier can be interpreted in different ways.

Given a targeted function type with n parameters, a set of potentially applicable methods is identified:

ReferenceType :: [TypeArguments] Identifier has two different arities, n and n-1, are considered, to account for the possibility that this form refers to either a static method or an instance method.

A method reference expression of the form ReferenceType :: [TypeArguments] Identifier can be interpreted in different ways. If Identifier refers to an instance method, then the implicit lambda expression has an extra parameter with type of this compared to if Identifier refers to a static method. It is possible for ReferenceType to have both kinds of applicable methods, so the search algorithm described above identifies them separately, since there are different parameter types for each case.

Comparator.comparing method accept a Function<T,R extends Comparable<? super R>>. when you use String::compareToIgnoreCase that will reports error,because it has two parameters one is implicit this another is a comparing string of method parameter, so it is more like a BiFunction<String,String,Integer> not a Function<String,Integer>.

BiFunction<String, String, Integer> comparator = String::compareToIgnoreCase;
// you can't assign a BiFunction to a Function
// because one is incompatiable with another.
Function<String,Integer> function = comparator;

Stream.sort method accept a Comparator, and Comparator is more like a BiFunction<T,T,Integer> so it is compatiable with String::compareToIgnoreCase. on the other hand, they can be interchangeable. for example:

Comparator<String> primary = String::compareToIgnoreCase;
BiFunction<String, String, Integer> comparator1 = primary::compare;
Comparator<String> comparator2 = comparator1::apply;

you can using comparing(String::toLowerCase) instead, it is equalivent to String::compareToIgnoreCase, for example:

// String::compareToIgnoreCase
listDevs.sort(String::compareToIgnoreCase); 

// comparing(String::toLowerCase)
listDevs.sort(comparing(String::toLowerCase))