Well, in essence they are the same program... only HeroStats (HS) is far more statistically oriented. They use the same engines to get the information.
Put it this way, if you want ALL kinds of info (stored locally on your own machine) AND all your badge and character basic info on CIT, use HeroStats. Via this link, it will show you how to set it up to update CIT (
Link).
If you're just looking to verify some badges and update your character info while having a reasonably smaller toll on your system's resources, use TNT: Glycerine.
Regarding the in-game, there is really no need for Glycerine to have it. The only thing it displays are your badges obtained while verifying and playing and the basic info the game already displays for you.
You should never run both programs at the same time, there is a good chance it will crash your game.