I spoke with some LDS youngsters who came to my door some time back. They're friendly. I learned that they do not like being referred to as "Mormon" but instead prefer "LDS". For them, being called Mormon is derogatory.
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CNN's web site had a piece on this yesterday: https://www.cnn.com/2023/04/29/us/mormon-beliefs-explained-c...
An initial split occurred before leaving Missouri with a large number of followers including Joseph Smith's mother and other family members (as I recall) choosing to follow James Strang to Beaver Island instead of Brigham Young to Utah.
That settlement was forcibly broken up, but it's an interesting story. You can google James Strang, (The King of Beaver Island) to read more on it. That church is still around as well and claim to be the true inheritors of the teachings of Smith.