American depositary receipts (ADRs) allow foreign equities to be traded on U.S. stock exchanges; in fact, this is how the stock of most foreign companies trades in U.S. stock markets. ADRs are issued by U.S. depositary banks, and each one represents one or more shares of a foreign stock, or a fraction of a share. When you own an ADR, you have the right to obtain the foreign equity it represents, although most U.S. investors find it easier to own the ADR.
For example, let's say that shares of CanCorp (a fictitious Canadian company) sell on the Toronto Stock Exchange for C$5.75 (US$5). A U.S. bank buys a number of shares and sells ADRs at a ratio of 2:1. Therefore, each ADR represents two shares of CanCorp and thus should sell for US$10.
ADRs are held in the vaults of the U.S. banks that issue them, although the shares they represent are actually held in the home country of the foreign-based corporation by a representative of the U.S. depositary bank. ADRs simplify the process of exchanging foreign shares: since it is only the receipts that are traded, investors do not need to worry about any exchange rate differences or the need to open special brokerage accounts. Furthermore, ADRs entitle investors to all dividends and capital gains.
An American depositary share (ADS), on the other hand, is the actual underlying share that the ADR represents. In other words, the ADS is the actual share trading, while the ADR represents a bundle of ADSs. For example, if a U.S. investor wanted to invest in CanCorp, the investor would need to go to her broker and purchase a number of ADRs that equal to the amount of CanCorp shares that she wants. In this case, the ADRs are the receipts that the investor has to purchase, whereas the ADSs represent the underlying shares (CanCorp) in which she invested.
To learn more, see our ADR Basics Tutorial, What Are Depositary Receipts? and What parties are involved in the creation of an American depositary receipt?