It's even more schizophrenic than usual at the minute. The airline has about 7 brands, British Midland, bmi british midland, bmi, flybmi, bmi British Midland International and so on. Just pick one and stick to it!
To me the new branding is a mouthful "bmi British Midland International, in association with our Star Alliance partners..."
The 5 brands mentioned is hardly 7.
British Midland was the old name for the airline, before being rebranded to bmi british midland & then finally bmi.
Flybmi is the website address only.
bmi - British Midland International is now being used as years later people still think bmi & British Midland have no relation.