How to get time difference between two timestamps in seconds with jQuery?

assuming you parse the string into JavaScript date object, you can do (date2 - date1)/1000

to parse mysql format timestamp, just feed the string into new Date():

 var d2 = new Date('2038-01-19 03:14:07');
 var d1 = new Date('2038-01-19 03:10:07');

 var seconds =  (d2- d1)/1000;

fix of edit 2 in the question:

<script type="text/javascript">
$(function(){
var d2 = new Date();
var d1 = new Date("2014-02-02 23:54:04");
$("a#timedif").html("Diff. Seconds : "+((d2-d1)/1000).toString());
 });

If you are okay with that plugin you can modify it a little bit to work with seconds only

  var words = seconds < 45 && substitute($l.seconds, Math.round(seconds)) ||
    seconds < 90 && substitute($l.minute, 1) ||
    minutes < 45 && substitute($l.minutes, Math.round(minutes)) ||
    minutes < 90 && substitute($l.hour, 1) ||
    hours < 24 && substitute($l.hours, Math.round(hours)) ||
    hours < 42 && substitute($l.day, 1) ||
    days < 30 && substitute($l.days, Math.round(days)) ||
    days < 45 && substitute($l.month, 1) ||
    days < 365 && substitute($l.months, Math.round(days / 30)) ||
    years < 1.5 && substitute($l.year, 1) ||
    substitute($l.years, Math.round(years));

with this part, go only with converting to seconds

see the fiddle: http://jsfiddle.net/zGXLU/1/