Let me offer some perspective on why we added this feature to the language, when clearly we didn't strictly need to (all methods refs can be expressed as lambdas).

Note that there isn't any right answer. Anyone who says "always use a method ref instead of a lambda" or "always use a lambda instead of a method ref" should be ignored.

This question is very similar in spirit to "when should I use a named class vs an anonymous class"? And the answer is the same: when you find it more readable. There are certainly cases that are definitely one or definitely the other, but there's a host of grey in the middle, and judgment must be used.

The theory behind method refs is simple: names matter. If a method has a name, then referring to it by name, rather than by an imperative bag of code that ultimately just turns around and invokes it, is often (but not always!) more clear and readable.

The arguments about performance or about counting characters are mostly red herrings, and you should ignore them. The goal is writing code that is crystal clear what it does. Very often (but not always!) method refs win on this metric, so we included them as an option, to be used in those cases.

A key consideration about whether method refs clarify or obfuscate intent is whether it is obvious from context what is the shape of the function being represented. In some cases (e.g., map(Person::getLastName), it's quite clear from the context that a function that maps one thing to another is required, and in cases like this, method references shine. In others, using a method ref requires the reader to wonder about what kind of function is being described; this is a warning sign that a lambda might be more readable, even if it is longer.

Finally, what we've found is that most people at first steer away from method refs because they feel even newer and weirder than lambdas, and so initially find them "less readable", but over time, when they get used to the syntax, generally change their behavior and gravitate towards method references when they can. So be aware that your own subjective initial "less readable" reaction almost certainly entails some aspect of familiarity bias, and you should give yourself a chance to get comfortable with both before rendering a stylistic opinion.

In many scenarios, I think lambda and method-reference is equivalent. But the lambda will wrap the invocation target by the declaring interface type.

For example

public class InvokeTest {

    private static void invoke(final Runnable r) {
        r.run();
    }

    private static void target() {
        new Exception().printStackTrace();
    }

    @Test
    public void lambda() throws Exception {
        invoke(() -> target());
    }

    @Test
    public void methodReference() throws Exception {
        invoke(InvokeTest::target);
    }
}

You will see the console output the stacktrace.

In lambda(), the method calling target() is lambda$lambda$0(InvokeTest.java:20), which has traceable line info. Obviously, that is the lambda you write, the compiler generates an anonymous method for you. And then, the caller of the of the lambda method is something like InvokeTest$$Lambda$2/1617791695.run(Unknown Source), that is the invokedynamic call in JVM, it means the call is linked to the generated method.

In methodReference(), the method calling target() is directly the InvokeTest$$Lambda$1/758529971.run(Unknown Source), it means the call is directly linked to the InvokeTest::target method.

Conclusion

Above all, compare to method-reference, using lambda expression will only cause one more method call to the generating method from lambda.