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.

Yeah, operations is kind of where engineering's best practices go out the window for practicality haha.

We used to tilt the spacecraft when doing inclination burns so that we could get a little bit of intrack delta-v to even out our orbit. I always thought that was delightfully janky.