Assuming a) you have SEF URL's enabled, and b) you've assigned your modules correctly this is usually caused by an SEF URL conflict.
What causes the problem?
Joomla's 'raw' URLs are a long string of characters starting index.php?option=blah&view=blah&blah etc - in fact this URL is a query string that tells Joomla what content to return, together with any display options you've set. Because you can assign templates and modules to different pages, you can sometimes end up with several different "views" of the same page. When Joomla SEF is enabled it maps the various "views" to a single SEF URL to eliminate undesirable duplicate pages, which aren't good from an SEO perspective. Unfortunately this view may not be the one you expect or want! So you need to tell the SEF component which one to use.
If you are using the Joomla core SEF function you can't easily change any mis-mapping, but if your site has one of the advanced SEF management components such as sh404SEF or JoomSEF installed, the "fix" can be quite straightforward.
To correct any mis-mapping...
To manage the module assignments and SEF URLs, you'll first need to find the Itemid for the menu item you used to assign the module(s).
In the Menu Manager, select to the relevant menu. This will list the menu items. Make a note of the number in the far right ID column.
Go to Components > sh404SEF > SEF URLs
Search for the SEF URL that's displaying incorrectly. If there's an orange box with a number showing in the "Duplicates" column for the URL, that's 99% likely to be why you aren't seeing the right modules displaying.
Click on the orange box to open the duplicates options pop-up. Look for the non-SEF URL with the Itemid=### that matches the menu item id number you noted. Click on the star icon in the Main column to select that version of the URL as your preferred option.
If there is more than one URL with that Itemid, that means you have more than one set of module/template assignments to that URL. If that's the case, you might need to do a little bit of trial and error to check you've got the right one.
In JoomSEF, go to ARTIO JoomSEF > Manage SEF URLs
Use the filter to find the SEF URL that's incorrect. If there are duplicates, all will be listed, but the primary one will be the one showing Hits. Click on it that one open the editing page.
In the Itemid box, enter the menu item id number and save the record.
If you have duplicate views for that same Itemid, you may need to delete the duplicates to force your new URL to take effect. Note this won't delete any content, just the URL mapping record.