Transfer agency is the name given to the work done by a transfer agent: keeping the official record of who owns a fund's or company's securities and processing the transactions that change it. The main entry describes the role, its regulation and the firms that perform it.
The two terms differ in emphasis. "Transfer agent" names the appointed firm; "transfer agency" names the function or the business line, and is the usual wording in the investment funds industry, especially in Luxembourg, Ireland and the United Kingdom. In that setting it covers maintaining the investor register, carrying out anti-money laundering checks on new investors, handling orders through subscription processing and redemption processing, paying distributions and sending statements.
Transfer agency is commonly outsourced to a specialist provider and is often bought together with fund administration, although the two are distinct: administration values the fund, while transfer agency deals with its investors. For company shares the equivalent work is more often described as registrar services.