Notify user on browser close only

Note that in your code, you're using onbeforeclose, but the event name is beforeunload, so property is onbeforeunload, not onbeforeclose.

I just want to work this code only for browser refreshing and closing. Is there a way to catch the refresh or browser cosing so that can use it.

No. Instead, you'll have to capture each link and form submission and either set a flag telling your onbeforeunload handler not to return a string, or removing your onbeforeunload handler (probably the flag is cleaner).

For example:

var warnBeforeClose = true;
function unloadPage(){
    if (warnBeforeClose) {
        return "Your changes will not be saved.";
    }
}
window.onbeforeunload = unloadPage;

// ...when the elements exist:
$("a").click(dontWarn);
$("form").submit(dontWarn);
function dontWarn() {
    // Don't warn
    warnBeforeClose = false;

    // ...but if we're still on the page a second later, set the flag again
    setTimeout(function() {
        warnBeforeClose = true;
    }, 1000);
}

Or without setTimeout (but still with a timeout):

var warningSuppressionTime = 0;
function unloadPage(){
    if (+new Date() - warningSuppressionTime > 1000) { // More than a second
        return "Your changes will not be saved.";
    }
}
window.onbeforeunload = unloadPage;

// ...when the elements exist:
$("a").click(dontWarn);
$("form").submit(dontWarn);
function dontWarn() {
    // Don't warn for the next second
    warningSuppressionTime = +new Date();
}

Update in 2017: Also note that as of at least a couple of years ago, browsers don't show the message you return; they just use the fact you returned something other than null as a flag to show their own, built-in message instead.