I'm looking for both an explanation of why and when you would use each system and what features differentiate a bug vs. issue tracking application.
Issue tracking systems usually integrate more with customers and customer issues. An issue could be "help me install this" or "How do I get the fubar into the flim flam." They could even be something like "I need an evalutation key for your software".
Bug tracking systems help you keep track of wrong or missing things from the program.
When looking at web systems, there is usually a big difference in focus, either helping customers or tracking problems with your software.