Most of a gallery's configuration settings are stored in the XML file (named 'config.xml' by default).
If you change only a few settings, then this is likely to be the only file that you will need to re-upload.
If you add new images to a gallery, then you will need to upload the new images (in the 'images' and 'thumbs' folders), too.
Certain options (such as the gallery's background color) are set in the gallery's embedding code (rather than the XML file), so you will need to re-upload the gallery's 'index.html' file if you change the background color.
Depending on the FTP program you use, you may be able to set it so that it uploads only new or modified files.
In doing so, you can tell the program to upload the complete gallery folder (rather than manually selecting files from within it) but only new and modified files will actually be uploaded to your web server.
If you are in any doubt as to whether or not the old files on your web server are being overwritten, try deleting them first before uploading the new or modified files in their place.
After uploading, try clearing your browser's cache before reloading your gallery to ensure that your browser fetches and uses the most recent gallery files from your web server. (Refreshing the page may not be enough.)