It seems a given that Ships and Boats have different but related control systems, since you can use Piloting skill for both, but have to choose a specialization.
My guess?
Automatic controls would be similar to what we get in Star Trek - buttons to align the ship's hull to certain reference headings (orbit prograde, retrograde, etc., and target-relative modes like 'facing target', 'docking orientation', 'facing away from target' and 'computed interception' and 'manual override'. The pilot would select an orientation mode and maybe run various course management commands (intercept, dock, orbit shaping, etc.), as well as having manual controls to input exact headings and trigger thruster firing.
Where the Piloting skill comes in is selecting the right programs, running them at the right time, and inputting parameters into the system so that it makes the right choices. Pilot-0, and you know which programs are available and when to run them so that you can get the ship to and from port without breaking anything. Pilot-1, and you have enough experience to know which settings works best and can handle unusual situations. Pilot-2+ and you probably have a set of custom presets and know enough about how the programs work to make the system dance for you with some additional manual control when needed.
Manual controls in human ships would likely be a 3-axis joystick for controlling orientation (yaw/pitch with right/left, and roll by twisting the stick), a throttle for the main propulsion system, and a 3-axis joystick for fine control, like docking. Taking a cue from the "orbiter" sim program, they might have an equivalent to the helo's collective which would activate the antigrav lifting system for use in a gravity well, but IMHO unless it was a specifically streamlined craft, it would probably just get by with X,Y,Z thrust controls.
All spacecraft would be fitted with inertial guidance and gyroscopic orientation instruments (or their higher-tech equivalents - antigravity would monkey with IG systems like steel hulls did with compasses back in the 19th Century) as well as some simple docking and rendezvous sensors of some kind.
Boats, lacking powerful computers, generally use their manual controls, though must surely have automation assistance for orbit shaping and rendezvous.
Ship pilots would also be trained to use the manual systems too (and would need to use them for landing on worlds without automatic landing systems), but would also be more familiar with the usage of the automated flight programs, given that most ships are large and sluggish and generally follow predictable flight paths.
Frankly, with even the most anemic spacecraft able to generate 1G of thrust for long periods of time, the more sophisticated orbital calculations aren't necessary. Who needs a minimum-energy transfer orbit under those circumstances? That being said, certain rules of orbital mechanics would still be important for craft that spent a lot of time in orbit. However, I imagine that's "Navigation" not "Piloting".