UA, also note old Continental flights operate under United branding but have a CO code.
American Airlines is a member of an alliance called OneWorld. In that alliance, there are several airlines around the world. They include: British Airways (Great Britain) Cathay Pacific (Hong Kong)...
they are in a star alliance, as are UAL, USAIR, BA, etc.
Yes, Ted airlines is part of United airlines but it's a smaller branch of United airlines.
United Airlines is an airline company.