What is the difference between function() and ()=> function() in flutter?

So let's have a look at how these actually work!

Dart has a formal specification documented and you can have a look at it by clicking here. A function in Dart has to have a few qualities which are:

1. return type (optional but recommended)
2. name (required)
3. parenthesis right after the name (required)
4. a list of parameters (optional)
5. function body inside curly brackets or a single statement of function body in front of =>.

Your question is about point #5. The difference between {} and => function body is that the curly brackets allow you to write multiple statements separated with a semi-colon ; while the second approach shall just be one statement, ended with a single semi-colon ;.

Let's have a look at a few examples. Here is a simple log() function that allows you to log any Object instance to the debug console:

import 'dart:developer' as devtools show log;

extension Log on Object {
  void log() => devtools.log(toString());
}

Note how the function has a return type of void (point 1), a name called log (point 2), no parameters denoted by () (point 3 & 4) and a function body which is a single statement with => (point 5).

You could write the same function with curly brackets (point 5) instead of => like so:

extension Log on Object {
  void log() {
    devtools.log(toString());
  }
}

The result of which will be exactly the same as the previous implementation.

Now let's look at another example where your function has a return value and some parameters.

String fullName(String firstName, String lastName) {
  return "$firstName $lastName";
}

Since this function has simply one statement, the return statement and just one semi-colon, it could be re-written as an arrow function like so;

String fullName(
  String firstName,
  String lastName,
) =>
    "$firstName $lastName";

So I would say the unwritten rules are:

1. Use arrow-functions if the body of your function is simple to understand. You could even have multiple lines of code inside an arrow-function's body as long as it's understandable, it's OK to use.

2. Use function bodies with curly-brackets if your function's body is rather complicated, consisting of multiple perhaps un-related pieces of code.