Earlier quoted context omitted.
That's a convention, but hardly the convention. I used to work satellite navigation for NOAA. For the GOES sats we often used Intrack (Prograde/Retrograde), Crosstrack (Normal/Anti-normal), and Radial (Towards planet/away from). I don't think anyone really referred to any directions as "plus x" or "minus y"
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 u…
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.