Another way of doing this is checking what your target id is
var evt;
document.onmousemove = function (e) {
e = e || window.event;
evt = e;
}
$("#name_input").focusout(function (e) {
if (evt.target.id == "apply_name") {
//apply_name clicked
} else {
//focus out and applyname not clicked
}
});