I have been collecting medals and badges of the German veterans groups in America for many years. The field is huge, uncataloged and the German terminology and use of abbreviations can be a challenge even to someone who can read the German. Here is an example using the scan below. The cross on the left is black enamel on silver. The inscription “DEUTSCHER KRIEGER VEREIN S.F.” translates as German Soldiers (war veterans) Association San Francisco. The key word here is Verein which usually but not always implies a local group.
The next item is a similar cross inscribed “DEUTSHER KRIEGER BUND N.A.” which translates as German Soldiers League (or union) of North America. The word Bund used here usually but not always indicates an organization on a state or national level. This cross is suspended from a brooch of crossed cannons and two shields, one American and the other German. The front cannon is inscribed with the initials “D.M.V.E.” which probably means “DEUTSCHER MILITAER VEREIN E….” German Military (including peace time veterans) Association “ and the letter “E” which is an abbreviation for a place name that begins with that letter. In this case probably another place in California since the enameling on both crosses looks like the work of one manufacturer.