Give each button the same value for the name attribute, then check which value it has:
<input type="submit" value="Complete" name="submit">
<input type="submit" value="AddComment" name="submit">
if(isset($_POST['submit']))
{
switch($_POST['submit'])
{
case 'Complete':
// do "Complete" stuff here
break;
case 'AddComent':
// do "AddComment" stuff here
break;
default:
// handle invalid value here
}
}