SALT LAKE CITY — The president, according to Mormon doctrine, is literally a seer, a prophet — the president, that is, of the church. Usually American presidents have a somewhat lower reputation.


Now that Mitt Romney, an active Mormon, is aspiring to the more mundane office, new attention has come upon the faith that guides him. And much of that attention has been accompanied by controversy, confusion and concern about how Mormonism fits into American society.


For a glimpse of how Mormons see themselves, though, it’s worth visiting the Church History Museum of the Church of Jesus Christ of Latter-day Saints here. Created by believers, for believers, the museum shows how close to the center of American life Mormons consider themselves to be.


The gap is enormous between that perspective and the one embedded in the wider culture. The hit Broadway musical “The Book of Mormon” riotously mocks the church’s doctrine. The high-toned HBO soap “Big Love,” which ended last year, relished the complications of polygamy (once endorsed by the church and long since renounced). Reports of posthumous Mormon baptisms of Holocaust victims have fueled outrage. Accusations of extremism and murder appear in thrillers reaching back to Sherlock Holmes’s first case in “A Study in Scarlet.”


In January a poll of Mormons conducted by the Pew Research Center’s Forum on Religion and Public Life found that 68 percent of Mormons believe Americans don’t see Mormonism as “part of mainstream American society,” and that 46 percent believe there is “a lot of discrimination” against them. The church, which claims 14 million adherents worldwide, knows it has a perception problem, and it developed an ad campaign to counter it.


While Mormons have been prominent in politics — including the Speaker of the House, Harry Reid, Democrat of Nevada; and Mr. Romney’s father, George W. Romney, former governor of Michigan — and while there are growing lists of famous Mormons in American culture, the church’s temple rites are as closed to non-Mormons as Mecca is to non-Muslims. Little is popularly understood about a religion that traces its origins to the revelations granted a 14-year-old son of a farmer in 1820 in Palmyra, N.Y. Is Mormonism central to American life or at its margins?


The museum doesn’t provide a definitive answer, but it does supply considerable insight into Mormon culture and some of the tensions in this young religion.


The museum opened in 1984, and its core exhibition dates from that period. Its current director, D. Kurt Graham, is quick to point out its antiquated character. It has videos but no interactive screens. It has a diorama of nondescript farmland with a fragmented 20-minute audio program, aided only by lights shining on the plastic landscape. The overall story is incomplete. All of this, he says, will change with a planned overhaul during the next three years. But even if not up-to-date in museological style, the narrative covers the faith’s fundamentals.


The exhibitions open with allusions to the founding revelations — in this case, divine figures seen by the kneeling farm boy, Joseph Smith, as shown in a 1913 stained-glass window. Then, as we look at the upstate New York landscape, we listen to audio commentary outlining the milestones that led to the church’s founding: further divine visitations; a buried book written on gold plates in cryptic hieroglyphs; the inspired translation of those plates by Smith yielding the Book of Mormon; and rampant persecution of the community of believers, who claimed to be restoring true Christianity.


The strange thing is that aside from these displays the rest of the museum could almost be an account of the settling of the American West. We see a reproduction of a 19th-century covered wagon with a clever wooden odometer attached to its wheel, the street plan of a new city on a promontory along the Mississippi River in Illinois, paintings of wagon trains and battles, fragile objects carried on long migrations, a 19th-century printing press and artifacts of early commerce.


The narrative climaxes in evocations of small-town American life, including marching-band uniforms and commemorative ribbons. A diorama maps Salt Lake City’s early expanse. We learn of the first Mormon Temple’s construction and the growth of Mormon social institutions, and glimpse religious practices along with evidence of the faith’s expansion, shown in artworks from Africa, Asia and South America. On the second floor is an exhibit about the religion’s presidents, whose achievements are outlined.


There is a sense of triumph in this chronicle, emphasized by a statue of the Mormon angel Moroni blowing a trumpet at the view of the Mormon Temple offered through a window. The church’s handiwork in Salt Lake City is as much a part of the landscape as the snow-covered mountains in the distance.


But this museum is not a tale of religious evolution, nor is it a presentation of theological ideas. It is also not a version of “Lives of the Saints,” with accounts of miracles.


It is actually a kind of identity museum belonging to that ever-expanding genre as a celebration of a particular hyphenated American group, an exploration of its trials and a demonstration of its achievements. The museum shows how earthly a religion Mormonism is, how practical its actions have been and how intimately connected its history is to the American past. The printing press, the farm, depictions of the ordinary citizens who were the first church members — we see a vision of early American democracy. The covered wagon, the daring mapping of unknown territory: Mormon history is a version of the American pioneering myth.