Many packages available with GTK and QT versions. So, What is difference between them? Is there any difference in performance or working method?
In general, the difference from a user perspective should be purely cosmetic. Qt and GTK set themes independently (via, e.g.,
GNU/Linux tends to be more GTK oriented than Qt in the sense that the former is more commonly used, so you may want to prefer it when given the choice; an exception would be under KDE, which uses Qt for its own applications -- although none of these factors is very important.
A more significant issue would be in contexts with very limited RAM (as in, < 1/4 GB); in this case you would probably want the system to use exclusively GTK or Qt, but not both. On most modern desktops with gigabytes of memory, however, this is not a concern -- using both extensively might cost you an extra (wild guess) 50-100 MB.
Note that there are also different versions of both GTK (2 and 3) and Qt (3 and 4) still widely used but not backward compatible (so a Qt 3 application cannot use Qt 4 libraries). However, both versions may exist on a system at the same time and the most serious consequence of this would be the potential for confusion and a bit more memory bloat.
No, there is no difference in the internal structure of such programs. GTK and Qt are user interface toolkits and frameworks. They are libraries that the developers use to design graphical interfaces.
When a graphical (GUI) program is written, first its core internals are developed. This is what makes the program run. You never see the core, they simply execute in the background. On top of this core, a User Interface (UI) is designed.
Now, the developers could design the complete interface from scratch, or re-use designs made by others. Re-using design has a major advantage. It allows all the programs in your computer to look similar. Hence, they use GUI toolkits. GTK and Qt are two extremely common GUI toolkits.
GTK is the standard toolkit for GNOME while Qt is used by KDE. From the user's point of view, it's just the looks that differ. The program remains the same at heart.