Simple question for a noob. Is there a difference between these to variables?

var object1 = document.getElementById('myElement');
var object2 = $('#myElement');

Also, am I able to run normal js stuff on object2? For example, if #myElement is a <textarea> can I do:

object2.value = "fill in with this text";

or, must I do: 

$(object2).val('fill in with this text');

or, is there yet a better way?

javascript jquery
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