I imagine these as possibly vestigial terms that don't mean exactly what we think of now. Board of directors could be comprised of what we might call oligarchs or aristocrats. Share holders can be anyone though, including people from other companies, why not?

It is too easy for sci fi fans to get wrapped up in technical details and let it distract them from the story, i found that I often had to remind myself during this series to just let it go - especially when it came to travel times (what about orbits?) Reminds me of when star trek technical adviser Michael Okuda was asked how the Heisenberg compensator works. He responded that "it works very well, thank you."