I like to consider a few similar terms.
Mormon
Christian
Hindu
Muslim
Catholic
Baptist
Starting at the bottom, is a Baptist someone who is part of a belief system, or a member of a specific church? Actually, this term may be the hardest to actually identify, as there is very little actual structure in Baptist churches.
Is a Catholic a member of a church, or someone who participates in a belief system? It is possible to say that a person must be a member of a specific church to be a Catholic, but that is not actually completely true. There are several different types of Catholic churches, all with very similar structures and all looking to the Pope for their spiritual guidance. There is the Roman church, an Ethiopian church, and an Eastern church with slightly different structures and philosophies (and no, I am not discussing the Orthodox churches here, but actual Catholic churches and belief systems).
Is a Muslim someone who is a member of a specific church, or someone who participates in a belief system? How about a Hindu? A Christian?
Perhaps it is obvious what I am getting at. We have all sorts of Christians telling us that we are not Christians, since our belief system is different than theirs. We frequently object to them excluding us, yet it is obvious that a lot of us think nothing of excluding others based on the same type of arrogance. Mormonism is a belief system. As much as the LDS church wants to "own" the name (and bury it if possible) it just doesn't fit. There are quite a few different groups, as well as independent people, who can make excellent defense that their belief systems fit at least as well as the LDS church's with the specific teachings of Joseph Smith. When we argue that they should be excluded based on their small differences, we sound just like the bigoted Christians that we so hate to hear.
Not all Mormons are LDS. That's a fact. LDS say they are the only mormons, but it's not true. Historically, the church "ended" with Joseph and a bunch of groups claimed to be the "one church" Joseph founded. Obviously not all can be right. And just because of our beliefs we assume that the LDS is the right one, and therefore deny the others that they are mormon because they belief different.
Mormonism includes about 156 different churches. It's not right to claim only the LDS can be "Mormon." In fact, theologians worldwide can tell you that many a fundamentalist mormon group is closer to the doctrines Joseph Smith preached than the modern LDS church. That's a fact regardless of how you interpret/explain it. And about the modern society definition, a) it's irrelevant, and society does think of Mormons as fundamentalists, not mainstream LDS.
And if you want to know churches that want to be called Mormon: Kingston Clan, FLDS and AUB come to mind.
The problem with this thread is that we really haven't established what the definition of Mormon is?
What is the definition of Mormon?
For me the Definition of Mormon is the Church of Jesus Christ of Latter-Day Saints.
From Dictionary.com and from Websters make this connection in there definition.
IF we are going to go by some different definition of Mormon's then that would need to be stated so we are clear on the meaning your talking about.
Edited: tubaloth on 4th Oct, 2009 - 6:06am
That is probably the whole problem. You define the word 'Mormon' to refer to the Church. However, the Church spent a couple of decades telling its members, and the world, that it was NOT the Mormon Church, and it tried very hard to completely disassociate itself from the word.
A lot of us look at the long view, and see a whole culture and philosophy that is based upon the Book of Mormon and the teachings and actions of Joseph Smith. We see that the Church is significantly different in teachings, theology, and practice from the time of Joseph Smith and Brigham Young.
Here is the definition from Wikipedia.