Government corporations
A few federal entities are built to act like businesses, earning revenue, run by boards, and meant to stand somewhat apart from the annual budget fight.
What makes a government corporation
Congress creates a government corporation to carry out a business-like function. It is usually funded substantially by its own revenue and governed by a board rather than a single department head, giving it more managerial flexibility than a typical agency.
Ones you already use
The Postal Service runs on postage; the FDIC on premiums paid by insured banks; Amtrak on fares plus a federal subsidy; the Tennessee Valley Authority on electricity sales; the Export-Import Bank on loan fees.
Why the form is used
It lets the government run commercial operations with business-like flexibility and a buffer from year-to-year appropriations, at the cost of somewhat less direct political control. Self-funding is part of what makes several of them among the most insulated entities in government.
Still public, still accountable
They remain federal entities bound by their enabling statutes and subject to audits, congressional oversight, and (usually) presidential appointment of their boards. Business-like is not the same as private.