I live in Washington DC. Here's a sample ballot (PDF). We vote for a Delegate to the House of Representatives. The incumbent, Eleanor Holmes Norton, is a local celebrity. Why do we have a separate vote for the "United States Representative"? If Washington DC became a state, we would have one member of the House of Representatives. In the state of Washington DC, would Eleanor Holmes Norton have to step down and be replaced by the United States Representative? Is there an historical reason the Delegate doesn't also serve as the United States Representative?
DC has two "shadow senators" and one "shadow representative" whose job is to represent its interests in Congress. It based this idea off of what various territories did as they approached statehood; they elected the people who would be their congressional delegation once they became states, and in the meantime those people advocated for the territory's interests. Separately, DC and the 5 inhabited territories have nonvoting delegates in the House so that the people who live there at least have some voice.
As far as the DC government is concerned, the shadow senators and shadow representative are US Senators and a US Representative. Sure, they aren't yet seated in Congress, but that's just pending DC statehood. They're still the state's congressional delegation. On the ballot, they're listed as Senators and a Representative. As far as everyone else is concerned, DC has one delegate and three people who play make-believe.
The delegate is a House member. She's on committees (and can sometimes vote in committee hearings), can speak on the floor, has an office on Capitol Hill and a professional staff, draws a salary, and can do constituent service. Even though she doesn't have a floor vote, she has everything else a full House member gets. In contrast, the shadow delegation is unpaid and has no staff. Their offices are in DC city hall, not on Capitol Hill. They can't speak on the floor of Congress (although shadow senators have some level of privileges for the Senate dining room). In practice, the shadow delegation is basically a group of elected unpaid lobbyists.