I do not see differences in bearing and course mode.

From the user manual:

https://www8.garmin.com/manuals/webhelp/instinct/EN-US/GUID-A8C5E65D-05C4-4F30-8693-501190635284.html

Bearing
Points in the direction of your destination.

Course
Shows your relationship to the course line leading to the destination

I can read and know where to find the instructions. I mean that in both cases the arrow on the map behaves as it showed only the course.

1340982 said:

I can read and know where to find the instructions.

Maybe you could choose a bit kinder tone when answering people trying to help you. Taking your anonymous numeric user name, and seeing that 95% of questions on this forum can be quickly resolved by checking the manual, it is hard to guess whether you did or did not check it first, when you did not mention it.

Linking to a manual that is not intuitive and you have to guess everything is also not helpful. But You right, I will describe the problems in my posts more thoroughly and accurately so that everyone can understand where the problem is again.

1340982 said:

Linking to a manual that is not intuitive and you have to guess everything is also not helpful.

Sorry, I thought the manual was quite clear, and that I could not describe it better, not being native english speaker, but if you want I can try anyway: 

Bearing is supposed to bring you to the destination regardless of the course track. Course mode is supposed to bring you back to the course track first.

However, in the firmware version 6.60 there is apparently a problem with the turn-by-turn navigation, and since, due to the confinment it is difficult to test it, I cannot exclude that the course mode in that version does not work as it is supposed to

So if the destination is in a different direction than the current course direction, should I see the differences? Because I don't see the difference in these modes on my watch,  it still shows the direction of the course.

Maybe you'll see more difference when you get considerably off the track.

In my opinion, this is indeed one of the points where the manual lacks clarity. It also puzzled me.  "Show your relationship" is a really vague notion of the type of information being provided. It may mean anything and everything. It probably means that it will direct you to the point of the course line that is closest to you, but it might really mean many other things. I had planned to experiment, to try to figure it out beyond any doubt, but I never got to do it, given that I do not use courses. Therefore, I never got the bottom of this. Do you think (or know for a fact) that it in fact directs you the point of the course line closest to you? (Which makes sense; but why don't they just say so :) ?)

Today I checked and in both modes step off the path by about 50 m causes the change of the arrow pointing mode to the final position of the course. I want to emphasize again in both modes, which is different behavior than the manual says.

As I wrote, the current v6.60 has a bug, where the turn-by-turn navigation and hence likely also the course mode do not work as intended. Garmin is investigating it, so we can expect a fix in the next release. I would either wait with the tests for then, or downgrade to the v5.70