Specifically, in real-world use, I would think that "course" and "heading" tend to imply a vector of movement, while "bearing" and "direction" might refer only to which way one is facing.
I am looking for two words to correctly assign to these physical components of a vehicle. I suppose I may be looking for military, or naval terminology.
For example, if you were in a submarine, being buffeted by currents, so your vessel was being pushed sideways, how would you correctly say, "we are being pushed east but we are facing north?" Would it be correct to say "we are bearing 0°, but our heading is 270°?" It doesn't sound correct.
Edit
As I note in a comment below: when I clumsily wrote that I was "looking for two words to correctly assign to these physical components of a vehicle," what I meant was, single-word attributes to distinguish between the direction a vehicle was facing, and the actual direction the vehicle was moving in, voluntarily or not.
Best Answer
Bearing is regularly defined as the direction (relative to true north) in which your destination lies. If you could go in a straight line to your destination, this would be the most direct way of getting there.
You also have relative bearing, where the front of the vehicle is considered "north"; you'll see this when pilots claim, for example, that something is "at your 3 o'clock"; in naval terminology, port (left) and starboard (right) are always relative to the bow (front of the vessel).
Heading is the direction your face/nose/front/bow is currently pointing at (relative to true north), assuming default movement by your vehicle's impulse mechanism is forward. If there are no obstacles between you and your destination, and nothing aside from your vehicle's own impulse mechanism is moving it, heading should always be equal to bearing.
Course describes the entire planned route to get to your destination. A course correction implies that your planned route encountered an obstacle, and that you have to correct that plan.
As an example, let's assume a car is the vehicle, and it's navigating in a standard grid-like street structure. If you're at point (0, 0) with your car facing north and your destination is at (3, 3), your course would be "Three blocks north, then three blocks east". Your bearing at the start of your journey would be north-east, and your heading would be north, since that's the way your car is facing.
After you travel three blocks north, you're stopped at a red light. You should plan to turn right, to change your heading to east, since your bearing is now east. Your remaining course is "3 blocks east".
In aviation, where winds can and often will push you off-course, heading is rarely equal to bearing when the total travel distance is large. This makes for frequent course corrections to account for wind.
In my opinion, direction is the most basic term of all, and describes a directed vector between two points.
For your example, it seems like the proper phrasing would be "We are heading north, but we're being pushed off-course eastwards."