Previously Twitizer used the Twitter Username (or screen name) as identifier of the user and its content, but as Username can be changed it’s not a trustworthy identifier, so Twitizer is now using the unique (and hopefully never-changing) Twitter user ID instead.
The biggest practical difference is that if you change Username on Twitter now, you will still be able to access content you’ve created under your old Username.
Other than that everything should work as before.
Also, note that each time you Login, Twitizer will update your profile information, including Username, Name, Picture, Bio, Location and Web.