Clarification on Invoking a Function vs. Referencing a Function?

From my understanding:Invoking a function means executing the function and getting its return value.

Referencing a function means treating the function as a value without executing it, e.g., passing it as an argument to another function without the parentheses.
Could someone provide more in-depth information or examples on:

The practical scenarios where referencing a function is essential(in real world app if possible)

How callbacks and higher-order functions utilize function references.

Any potential pitfalls or common mistakes when handling function references and invocations.

fun greet(name: String) = "Hello $name!"

// simplified version of the real map implementation
public inline fun <T, R> List<T>.map(transform: (T) -> R): List<R> {
    var result = mutableList<R>()
    for(t in this) {
        result += transform(t) // short for: transform.invoke(t)
    return result

fun main() {
   val greetings = listOf("Peter", "Paul", "Mary").map(::greet)

map expects a function (T) -> R, and in our case T is String, so the greet function fits the bill. Note that we don’t use curly braces after map, as we don’t want to define a lambda as usual, but just pass a function as a normal argument. When map wants to use the function passed as “transform”, it just calls it with an argument (directly or via invoke, doesn’t make a difference)