There is a Treaty Trader Visa which is the E-1. The E-2 is a Treaty Investor Visa. E visa issuance is generally based on a reciprocal Treaty of Friendship, Navigation and Commerce. Oftentimes these treaties provide for both E-1 and E-2 visas; some provide for just E-1 or E-2 visas. E-2 visas can also be the result of an agreement between the U.S. and another country called a “Bilateral Investment Treaty” (BIT).
Someone from a country with which we have an E-1 treaty is allowed to open a company in the U.S. that trades principally back and forth with their home country; not solely, but principally. Generally, the company must first initiate trade/business before the E-1 visa will be issued. However, as mentioned, the E-1 requires that there be a history of trade between the U.S. and the foreign country before visa issuance.
With the E-2 you can get the visa once the U.S. business is legally formed and capital is invested or in the process of being invested, before you’ve even done business, just as you’re getting off the ground.
The E-3 visa is specific to Australian citizens and is more akin to the H-1B visa. It is the result of the Australian-United States Free Trade Agreement.