There are different conventions, yes. Even for the shuttle I've seen +z point in the opposite direction in some documents. I work in systems engineering so I'm less exposed to terms used in operations and more in discussions about which part of the spacecraft things are located.

Actually I work on rovers and it's a perennial debate whether to follow spacecraft convention (+z is down) or automotive convention (+z is up). Then mechanical engineers will usually follow what is intuitive on the screen (+z is forward). This is because computer graphics convention is +z facing out of the screen.