Is this phrase always true?
$(\"p\").click(function(event) {
alert( event.currentTarget === this );
});
Is one method preferred over the o
Generally, yes, it will be the same. You can make it different by using $.proxy to manipulate the context, but in practice you probably never will.
$(document.body).on('click', $.proxy(function(e) {
console.log(this); // window
console.log(e.currentTarget); // document.body
}, window));
As to the other question, this is a native DOM element, whereas $(this) is a jQuery object wrapping that DOM element. The jQuery wrapper means you can run jQuery functions such as css, which are not available on native DOM elements.
And, to answer the precise wording of your question, event.currentTarget is normally equal to this, not to $(this).