Sata International is a subsidiary to Grupo Sata and was founded in the 1990's to provide international service by Sata. Their service includes several European Hubs, all of Portugal, and several North American cities as well.
They are now known as Azores Airlines - a change that was likely made for marketing purposes. So far, since the change I have found no difference aside from their new branding and an updated website.
Sata is owned by the regional Government of the Azores and the international service helps to bring some tourism to the Islands. As I understand it all of the flights are considered non regular chartered flights. Which is why it is still difficult to find information about Azores flights.
The international division of Sata has regular flights from many European and North American cities to João Paulo II Airport in Ponta Delgada (Sao Miguel) and a few directly to Lajes Field in Terceira.
I have listed the locations where Sata has direct flights to the Azores.
If you are looking for an inter-Island flight, Sata Air Azores handles flights within the Azores Islands. There are daily flights within all of the Islands in the Archipelago. But to get to the islands with Sata you can count on the following departure points.
There are daily flights from Lisbon.
There are several flights a week from Toronto and Boston to Ponta Delgada. There are also weekly flights from Montreal and Oakland to the islands.
There are several flights a week from Frankfurt to Ponta Delgada as well as weekly flights from Amsterdam, London and Manchester.