Are all people born in Nevada and California Americans? Yes!
Are all Americans, Nevadans? No!
Are all LDS members Christians? Yes!
Are all Christians, Mormon? No!
Are all Mormons, LDS? No!
Are all LDS, AUB, Kingston, etc Mormon? Yes
The funny thing is that the LDS church applies the logic of: We believe in the Bible, God the Father, Jesus Christ, the Atonement etc. The rest of the Christian community disagrees. The LDS church says: What part of The Church of JESUS CHRIST don't you get? Yet when it comes to the definition of Mormon, they do not like the same logic. hm... What part of we believe in Joseph Smith, the first vision, the [Book of Mormon], etc don't you get? Lastly, who actually left the teachings of Joseph Smith? The fundamentalists or the LDS church?
Robert the problem is that we need to let others know the true name of our Church which isn't the Mormon Church. When you introduce yourself to someone for the first time, you tend to tell them your name instead of your nickname, same thing applies here.