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If I had a super sticky wheel without any drifting, would the odom system always be the same like the map system?

An ideal environment would imply that the map and odom system would have had the same relations. But this isn't usually the case as the real world scenario would have many factors other than drifting that would act on the wheel.

the change from the odom system to the map system would be in a real case exactly the change of coordinates due to drifting movement?

Drifting would contribute a major part to the factors which you say are the real cause for the change of co-ordinates.

That would mean, that the only coordinates I have are those in the odom system?

Yes . You can still verify if there are any compensations added on to the navigation stack to compensate drift and other factors, but they aren't usually done as it would be different for each and every robot.

Try asking the last part as a separate question as it might have a better change of being answered.

If I had a super sticky wheel without any drifting, would the odom system always be the same like the map system?

An ideal environment would imply that the map and odom system would have had the same relations. But this isn't usually the case as the real world scenario would have many factors other than drifting that would act on the wheel.

 
the change from the odom system to the map system would be in a real case exactly the change of coordinates due to drifting movement?

Drifting would contribute a major part to the factors which you say are the real cause for the change of co-ordinates.

 
That would mean, that the only coordinates I have are those in the odom system?