"Two types" would be far too limiting for Whitman, who sought to contain "multitudes." In "Song of Myself," he uses himself and the wonders of his own body as a focal point from which he casts his gaze outward to explore the diversity of nature, starting with the smallest blades, or "leaves," of grass, the beauty of men and women, then moving on to the ethnic and cultural diversity of the United States and the unique character of each region.
If you insist on pursuing two representations of identity in the lengthy poem, you could argue that Whitman encourages the view of a self as the base from which one approaches and identifies with others ("I CELEBRATE myself, and sing myself, / And what I assume you shall assume, / For every atom belonging to me as good belongs to you"). So, democracy requires the recognition of a self, but a self that is connected to a communal whole.
Notable Whitman scholar, Ed Folsom, also explores American identity as a form of being that hovered between the "savage"--an agglomeration of Native American and pioneer instincts--and civilization, as represented in Eastern coastal cities and even in the hierarchical Southern slave societies, which were attempted to model Ancient Greece and Rome.
In section 16 of "Song of Myself," Whitman explores both this notion of the self in relation to the other, as well as the presences of both the "wilderness" and civilization in the American character:
One of the Nation of many nations, the smallest the same and the largest the same,
A Southerner soon as a Northerner, a planter nonchalant and hospitable down by the Oconee I live,
A Yankee bound my own way ready for trade, my joints the limberest joints on earth and the sternest joints on earth,
A Kentuckian walking the vale of the Elkhorn in my deer-skin leggings, a Louisianian or Georgian,
A boatman over lakes or bays or along coasts, a Hoosier, Badger, Buckeye;
At home on Kanadian snow-shoes or up in the bush, or with fishermen off Newfoundland,
At home in the fleet of ice-boats, sailing with the rest and tacking,
At home on the hills of Vermont or in the woods of Maine, or the Texan ranch,
Comrade of Californians, comrade of free North-Westerners, (loving their big proportions,)
Whitman valorizes the United States, but in declaring it "one of the Nations of many nations," he is not elevating it above any other country, but his use of capitalization does suggest that he gives it primacy, for, he is an American with a unique love for his own country. In Whitman's view, the smallest is of equal value to the largest, which could be read as an early anti-Imperialist sentiment.
Then, he looks more closely at the nation's regional idiosyncrasies, but roots each representative--the Southern planter, the Yankee trader, the deerskin-wearing Kentuckian, the bayou boatman, and the Northern fisherman--to his particular connection to and dependency on nature, which he has adapted to meet the ends of civilization, particularly commerce, and survival.