Why Does Kotlin/JS Return Different Results for === Than Does Kotlin/JVM?

This is because of how the runtime handles it.

On the JVM, == maps to equals, and === maps to == (identity checking), as outlined here. Meanwhile, JavaScript's equals operators are weirder. If you decompile your code, you get this with JS:

kotlin.kotlin.io.output.flush();
if (typeof kotlin === 'undefined') { 
    throw new Error("Error loading module 'moduleId'. Its dependency 'kotlin' was not found. Please, check whether 'kotlin' is loaded prior to 'moduleId'."); 
}
var moduleId = function (_, Kotlin) { 
    'use strict'; 
    var equals = Kotlin.equals; 
    var println = Kotlin.kotlin.io.println_s8jyv4$; 
    function main(args) { 
        var value = 'something';
        println(equals(value.toUpperCase().toLowerCase(), value)); // NOTE: equals
        println(value.toUpperCase().toLowerCase() === value);      // NOTE: ===
    } 
    _.main_kand9s$ = main; 
    main([]); 
    Kotlin.defineModule('moduleId', _); 
    return _; 
}(typeof moduleId === 'undefined' ? {} : moduleId, kotlin); 
kotlin.kotlin.io.output.buffer;

Now, if you consider the equivalent Java code (slightly shortened and without Kotlin):

public static void main(String[] args){
    String value = "something";

    System.out.println(value.toUpperCase().toLowerCase().equals(value));
    System.out.println(value.toUpperCase().toLowerCase() == value);
}

toUpperCase().toLowerCase() creates a new object, which breaks the == comparison, which is identity checking.

While === is outlined as identity checking as well, a === b is true if a and b are strings that contain the same characters. As you can tell from the decompiled Kotlin code, Kotlin.JS compiles to primitive Strings, not String objects. Because of that, the === in JS will return true when you're dealing with primitive strings.