Agency relationships with clients versus Non-Agency relationships with customers

Agency relationship: Traditionally, the broker provides a conventional full-service, commission-based brokerage relationship under a signed listing agreement with a seller or "buyer representation" agreement with a buyer, thus creating under common law in most states an agency relationship with fiduciary obligations. The seller or buyer is then a client of the broker. Some states also have statutes which define and control the nature of the representation.
Agency relationships in residential real estate transactions involve the legal representation by a real estate broker (on behalf of a real estate company) of the principal, whether that person or persons is a buyer or a seller. The broker (and his/her licensed real estate agents) then becomes the agent of the principal.
Non-agency relationship: where no written agreement nor fiduciary relationship exists, a real estate broker (and his agents) works with a principal who is then known as the broker’s customer. When a buyer, who has not entered into a Buyer Agency agreement with the broker and buys a property, then that broker functions as the sub-agent of the seller’s broker. When a seller chooses to work with a transaction broker, there is no agency relationship created.
Transaction brokers
Some state Real Estate Commissions, notably Florida's after 1992 (and extended in 2003) and Colorado's after 1994 (with changes in 2003), created the option of having no agency nor fiduciary relationship between brokers and sellers or buyers. The transaction broker assists buyers, sellers, or both during the transaction without representing the interests of either party. They may be then regarded as customers.
As noted by the South Broward Board of Realtors, Inc. in a letter to State of Florida legislative committees"The Transaction Broker crafts a transaction by bringing a willing buyer and a willing seller together and assists with the closing of details. The Transaction Broker is not a fiduciary of any party, but must abide by law as well as professional and ethical standards." (such as NAR Code of Ethics)
The result was that in 2003, Florida created a system where the default brokerage relationship had "all licensees …operating as transaction brokers, unless a single agent or no brokerage relationship is established, in writing, with the customer" and the statute required written disclosure of the transaction brokerage relationship to the buyer or seller customer only through July 1, 2008.
In both Florida and Colorado's case, dual agency and sub-agency (where both listing and selling agents represented the seller) no longer exist.
Dual or limited Agency
Dual agency occurs when the same brokerage represents both the seller and the buyer under written agreements. Individual state laws vary and interpret dual agency rather differently.
Many states no longer allow dual agency. Instead, Transaction Brokerage (see above) provides the Buyer and Seller with a limited form of representation, but without any fiduciary obligations (see Florida law). Buyers and sellers are generally advised to consult a licensed real estate professional for a written definition of an individual state's laws of agency, and many states require written Disclosures to be signed by all parties outlining the duties and obligations.
If state law allows for the same agent to represent both the buyer and the seller in a single transaction, the brokerage/agent is typically considered to be a Dual Agent. Special laws/rules often apply to dual agents, especially in negotiating price.
In some states (notably MarylandDual Agency can be practiced in situations where the same brokerage (but not agent) represent both the buyer and the seller. If one agent from the brokerage has a home listed and another agent from that brokerage has a buyer-brokerage agreement with a buyer who wishes to buy the listed property, Dual Agency occurs by allowing each agent to be designated as “intra-company” agent. Only the broker himself is the Dual Agent.
Some states do allow a broker and one agent to represent both sides of the transaction as dual agents. In those situations, conflict of interest is more likely to occur.