"Line manager" is pretty standard business terminology. It mainly refers to the person that coordinates HR type functions whilst not directly managing a person. So in my case, I'm working in Singapore and report on a 'dotted-line' basis to the country manager, and also to the head of my discipline in Asia who is based in HK, but my line manager remains in London (as she signs off my leave requests and expenses!)

I imagine in the BA context if you are a member of crew your manager is whomever your CSD/CSM is on the day, whereas your "line manager" is a more permanent person responsible for your day to day admin, career progression, discipline and well-being.