The component GUIDs could be shared too. This is most likely the source of your problems. As a practice, you should NEVER copy a project and use to create a setup project for another similar product, this is the easiest way to miss updating some GUIDs that must be unique and have your packages behave incorrectly.
I don't know if InstallShield has the option, other tools do have it, but the recommended method is to create a project template from the first one (A), then create a new project from that template, case in which IS should make sure that you get new unique GUIDs for all sensitive areas from the package.