They are not at all related.
.add()
Add elements to the set of matched elements.
e.g.
If you want to do,
$('div').css('color':'red');
$('div').css('background-color':'yellow');
$('p').css('color':'red');
Then, you can do,
$('div').css('background-color':'yellow').add('p').css('color':'red');
Reference
.append()
Insert content, specified by the parameter, to the end of each element in the set of matched elements.
$('div').append('p');
will append selected p on all selected div in dom.
Reference