jquery .html() vs .append()

They are not the same. The first one replaces the HTML without creating another jQuery object first. The second creates an additional jQuery wrapper for the second div, then appends it to the first.

One jQuery Wrapper (per example):

$("#myDiv").html('<div id="mySecondDiv"></div>');

$("#myDiv").append('<div id="mySecondDiv"></div>');

Two jQuery Wrappers (per example):

var mySecondDiv=$('<div id="mySecondDiv"></div>');
$('#myDiv').html(mySecondDiv);

var mySecondDiv=$('<div id="mySecondDiv"></div>');
$('#myDiv').append(mySecondDiv);

You have a few different use cases going on. If you want to replace the content, .html is a great call since its the equivalent of innerHTML = "...". However, if you just want to append content, the extra $() wrapper set is unneeded.

Only use two wrappers if you need to manipulate the added div later on. Even in that case, you still might only need to use one:

var mySecondDiv = $("<div id='mySecondDiv'></div>").appendTo("#myDiv");
// other code here
mySecondDiv.hide();

Whenever you pass a string of HTML to any of jQuery's methods, this is what happens:

A temporary element is created, let's call it x. x's innerHTML is set to the string of HTML that you've passed. Then jQuery will transfer each of the produced nodes (that is, x's childNodes) over to a newly created document fragment, which it will then cache for next time. It will then return the fragment's childNodes as a fresh DOM collection.

Note that it's actually a lot more complicated than that, as jQuery does a bunch of cross-browser checks and various other optimisations. E.g. if you pass just <div></div> to jQuery(), jQuery will take a shortcut and simply do document.createElement('div').

EDIT: To see the sheer quantity of checks that jQuery performs, have a look here, here and here.

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innerHTML is generally the faster approach, although don't let that govern what you do all the time. jQuery's approach isn't quite as simple as element.innerHTML = ... -- as I mentioned, there are a bunch of checks and optimisations occurring.

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The correct technique depends heavily on the situation. If you want to create a large number of identical elements, then the last thing you want to do is create a massive loop, creating a new jQuery object on every iteration. E.g. the quickest way to create 100 divs with jQuery:

jQuery(Array(101).join('<div></div>'));

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There are also issues of readability and maintenance to take into account.

This:

$('<div id="' + someID + '" class="foobar">' + content + '</div>');

... is a lot harder to maintain than this:

$('<div/>', {
    id: someID,
    className: 'foobar',
    html: content
});