1.JQuery is a lightweight client side scripting library while AJAX is a combination of technologies used to provide asynchronous data transfer 2.jQuery and AJAX are often used in conjunction with each other 3.jQuery is primarily used to modify data on the screen dynamically and it uses AJAX to retrieve data that it needs without changing the current state of the displayed page 4.Heavy usage of AJAX functions often cause server overload due to the greater number of connections made

AJAX is a way of sending information between browser and server without refreshing page. It can be done with or without library like jQuery.To compare them would be to compare apples and oranges.