Short answer
The Azores have nine islands, divided into three groups: Eastern (São Miguel and Santa Maria), Central (Terceira, Graciosa, São Jorge, Pico and Faial) and Western (Flores and Corvo). São Miguel is the largest and most populated; Corvo is the smallest. Inter-island travel is by plane or ferry, but ferry schedules are seasonal and weather-dependent, so always check ahead.
General information, not legal or tax advice. Rules and amounts change: confirm with official sources.