Beyond that there are no links whatsover between the two groups and insofar as 'what they actually do' in FM temples involves everything from reviewing the minutes of the last meeting, to discussing and passing a budget for the upcoming year, to organizing elections for lodge officers each calendar year, not to mention considering and vetting and evaluating potential initiates into the order. All very mystical and mysterioius stuff, lol.
That’s right. Joseph Smith believed the FM rites originated in Solomons temple (a common belief in the 1800s I think). He was a FM for a short time before they learned he was exporting their rituals to his own cult, and he was kicked out. Thus the Mormon narrative is that FM’s have a bastardized version of the proper ancient Jewish temple rituals, and Mormons have the ‘pure’ restored version.
From the outside it’s completely bananas. But I assure you, Mormons really and truly believe it deeply. It’s one of the strangest religions out there.