Hi rvsoo73,
1) If you have made the changes from the Business Catalyst admin panel, then saving the changes will update your page.
Also, the changes made in the Business Catalyst admin panel, can be synced with your Muse file.
However, this will sync all the changes that were made via the In-browser editing from Business Catalyst.
Following is an article on the In-browser editing:
http://www.adobe.com/inspire/2013/12/in-browser-editing-muse.html
After changes are made to the live site using In-Browser editing, your local .muse file no longer contains the same content as the live site.
To sync the changes to the muse file, launch Muse and open the site’s .muse file; and from the File menu, select "Sync with Web version"
2) If you have made the changes via Muse, then to update your site to business catalyst, you will need to publish the site.
To publish the site, select "Publish" from the "File" menu.
The following link might be helpful:
http://tv.adobe.com/watch/learn-muse/publishing-your-site-to-business-catalyst/
Regards,
Sonam