WASHINGTON — Most days the National Mall, a two-mile grassy expanse with the Capitol on its east end and the Lincoln Memorial on the west, is home to Frisbee players, museumgoers and joggers. On the Fourth of July, it hosted two distinct versions of America.

On the Capitol side Thursday afternoon, a smattering of mostly local residents, some carrying picnic hampers, waited in the humid weather for the traditional Independence Day concert featuring singer-songwriter Carole King, the National Symphony Orchestra, a special guest appearance by the Muppets and fireworks at nightfall.

On the Lincoln Memorial side, a raucous crowd of President Trump’s faithful, wearing red hats and plastic rain ponchos, pushing strollers, leaning on canes, and lugging lawn chairs, Chihuahuas and at least one Great Dane, began arriving more than six hours before Mr. Trump’s scheduled speech.