Two kinds of issuer sit under one label. FINRA Rule 6710(k) defines an "Agency" as a U.S. executive agency "that is authorized to issue debt directly or through a related entity, such as a government corporation, or to guarantee the repayment of principal and/or interest of a debt security issued by another entity," and carves out the Treasury itself. Paragraph (n) then borrows the definition of a government-sponsored enterprise from 2 U.S.C. 622(8): a corporate entity created by federal law that "has a Federal charter authorized by law," "is privately owned, as evidenced by capital stock owned by private entities or individuals," is directed by a board a majority of which private owners elect, and is a financial institution with power to lend for limited purposes and to "raise funds by borrowing (which does not carry the full faith and credit of the Federal Government)." A GSE is therefore a private company with a public charter, and its debt is the debt of a private company.
The charters say so, in the securities themselves. Fannie Mae's charter, 12 U.S.C. 1719(b), requires that "The corporation shall insert appropriate language in all of its obligations issued under this subsection clearly indicating that such obligations, together with the interest thereon, are not guaranteed by the United States and do not constitute a debt or obligation of the United States or any agency or instrumentality thereof other than the corporation," and 1719(d) imposes the same requirement on its mortgage-backed securities. Freddie Mac's charter, 12 U.S.C. 1455(h)(2), uses nearly identical words for "all of the obligations and securities of the Corporation." The Federal Home Loan Bank Act, 12 U.S.C. 1435, provides that "All obligations of Federal Home Loan Banks shall plainly state that such obligations are not obligations of the United States and are not guaranteed by the United States." The Farm Credit Act, 12 U.S.C. 2155(c), is the shortest: "The United States shall not be liable or assume any liability directly or indirectly thereon." Whatever the market assumes about how the government would behave if one of these entities failed, the legal position is printed on the paper.
Ginnie Mae is the exception, and it guarantees rather than issues. The Government National Mortgage Association does not sell bonds. Under 12 U.S.C. 1721(g)(1) it is "authorized, upon such terms and conditions as it may deem appropriate, to guarantee the timely payment of principal of and interest on" securities issued by approved issuers and "backed by a trust or pool composed of mortgages which are insured" by the Federal Housing Administration or insured or guaranteed under the veterans' and rural housing programs the statute names, and the same paragraph provides that "The full faith and credit of the United States is pledged to the payment of all amounts which may be required to be paid under any guaranty under this subsection." A Ginnie Mae mortgage-backed security is therefore the one class of agency security whose timely payment carries the same federal promise as a Treasury bond. A Fannie Mae or Freddie Mac mortgage-backed security, by the charters quoted above, does not.
Mortgage-backed securities are the largest agency product. Fannie Mae, Freddie Mac and Ginnie Mae exist to channel money into home lending, and the conforming loan page describes the first two as buyers of mortgages from lenders. The securities those mortgages become, pools whose holders receive the homeowners' principal and interest as it is paid, are what a total bond market fund holds under the heading of securitized or mortgage-backed debt, and what the Federal Reserve bought in large quantities during quantitative easing. This page names them; a mortgage-backed security has mechanics of its own, including the risk that homeowners refinance early, that are not covered here.
Registration exemption, and where the securities trade. The MSRB notes that agency securities "also are generally exempt from the registration and prospectus requirements of the Securities Act of 1933," so, like Treasury and municipal securities, they are sold on the strength of the issuer's own disclosure rather than an SEC-reviewed registration statement. Agency debt trades over the counter through dealers, and trades are reported to FINRA's Trade Reporting and Compliance Engine (TRACE) under the Rule 6700 series, which is why the FINRA definitions above exist. Agencies also issue short paper: Rule 6710(o) treats a discount note issued by an Agency or a GSE with a maturity of one calendar year and one day or less as a money market instrument.
Yield, and tax. Because most agency debt lacks the federal guarantee and trades in a smaller market than Treasuries, it generally yields somewhat more than a Treasury security of the same maturity; the extra yield is the market's price for the difference in backing and liquidity, and it varies with conditions rather than following any fixed spread. Interest on agency debt is taxable at the federal level. Its treatment for state and local income tax is not uniform across issuers: 31 U.S.C. 3124 exempts obligations of the United States Government from state taxation, but whether a given agency's or GSE's securities share that exemption depends on that entity's own statute, so it has to be checked issuer by issuer rather than assumed.