I think the original poster was identifying a well-known design "fault" in Joomla.
If a module is placed onto a front-page, category or section's blog-style (or list-style) page, then the module appears not only on that page, but also on the article page if you click through on an article.
Help is at hand though - check out MetaMod for Joomla on the Joomla Extensions Directory, which can help you to precisely place modules onto exact pages, e.g. excluding them from the article page that you click through to:
http://extensions.joomla.org/extensions/access-a-security/frontend-access-control/3391It's available for Joomla 1.0 and 1.5 (native).