I only recently learned this. Like the OP, I expected integration. I expected the brain functions to be within the MFD and it would simply send simple course/XTE sentances to the AP. At its core, an AP doesn't receive too much external information........or so I thought.
Peter
Then I'm not sure I explained it well, because I think it's more like you thought.
Here's how an AP works in "Nav" mode, which is what you use to navigate to a single waypoint, or to follow a sequence of waypoints, aka a route.
On the MFD/chart plotter you "activate" the waypoint or route. It sounds like Garmin calls this Go To and Route To. Coastal Explorer calls it "activating a route". I don't recall what Ray, Simrad, or Furuno call it.
When a route is activated on the plotter, it starts sending a few message that are really very simple. It basically reports the bearing and distance to the next waypoint, the name of the waypoint, and the cross track error (XTE). All this is calculated by the plotter based on your current position, and gets repeated every second or two. When you first activate the route, the plotter creates an imaginary "track line" from your current position to the waypoint, and the XTE is just how far off the line you are at the moment to the left or right. The plotter doesn't know and doesn't care if anyone is listening. This part is universal across every plotter I've ever seen, and the messages are completely standardized both on 0183 and N2K.
Assuming the AP starts out in standby, you now need to put it in Nav mode. That is done at the AP control panel. This, plus switching to Auto mode, or back to Standby is what has to be done at the AP control panel, not the MFD.... Unless.... you have the same brand MFD and AP. In that case most of the MFD vendors allow you to change the AP mode via the MFD. Otherwise you need to use the AP control panel.
Once in Nav mode, the AP now starts listening to those waypoint and XTE messages coming from the plotter. The AP will then steer the boat to keep it on the track line with some degree of precision. If the boat drifts too far off to one side as indicated by an excessively large XTE, the pilot will start to steer the other direction trying to bring the XTE back down to zero. It's really a very simplistic system. It's liek two people driving a car. One person (the plotter) watches the road and continually calls out the car's distance from the guard rails. The other person (pilot) has the wheel but is blindfolded, and steers the car based on the distances from the guard rails called out by the first person. Their job is to never get to too close to either guard rail.
It's also important to understand that the pilot really never knows anything about the route. All it ever knows about is the current waypoint and XTE info it's getting from the plotter. People often talk about downloading a route to the pilot, and that can lead you to think it's sending all the route info to the pilot, but it's not. It only ever knows about one waypoint at a time. The last waypoint is forgotten and the next waypoint is unknown. When a route waypoint it reached, the waypoint that's being sent to the AP suddenly changes to the next waypoint. Once the AP sees the change, it turns towards the new waypoint, and starts trying to reduce the XTE to get the boat onto the new track line.
Once you realize that the AP's only mission in life is to stay on the track line, you will understand some of otherwise unexpected things that pilots all do. For example, let's say you go into Auto mode to maneuver past a boat, then switch back to Nav mode. You probably aren't still on the track line when you do that, and the AP will turn to get back to it. Depending on how far off you are, the turn can be very aggressive, and is the cause of a lot of Crazy Ivans, or other unexpected sudden turns.
There are a couple of ways to get back on track gracefully. One is to do a "Reset XTE" on the chart plotter. This causes the plotter to compute a new track line from your current position. After doing that, you are now back on the line with a zero XTE, and the pilot just needs to adjust your course so you are heading for the waypoint. You'll want to hit Reset XTE immediately before resuming Nav mode. Otherwise, if the boat isn't already heading towards the waypoint, you will be accumulating XTE every second and the pilot will try to correct for that. My preferred method is to steer in Auto mode until you are heading towards the waypoint, then hit Reset XTE, then resume Nav Mode. That puts you on heading and on track when you engage Nav mode, and the pilot should take over gracefully.
The other way is to steer back to the original track mode until you are back on track and on heading, then engage Nav mode. But unless you deviated pretty far from course or really need to be on the original track, I find the first method works best.
Sorry for the long post, but I think this is a real mystery for a lot of people when it's actually a really simplistic system. You can also dig into your pilot's manual to learn about variations on some of these modes. For example, some pilots have setting where it will always steer towards the waypoint and ignore XTE. That eliminates the issue of getting back on track after a diversion, but the boat will side slip off the track based on wind and current. In some cases this is fine, but in others it's not.