In terms of functionality, there is no difference between the jQuery-x.x.x.js and jQuery-x.x.x-min.js (also called minified version). However this can play a vital role in the performance of the web page.
How it affects the performance?
jQuery-1.4.4.js file size is 178 KB as against its minified version jQuery-1.4.4-min.js that is only 76.7 KB in size. So when your page loads in the client?s browser if you are not using minified version, it loads 178 KB file that takes more time to load than 76.7 KB.