My ledger says I have 19 direct vassals but the upper-right corner says I have 10 vassals

I think that my vassals often control provinces outside my realm, but I have trouble understanding the upper-right corner. It says I have 10 vassals, but maybe it means only 10 vassals with big desmesnes. Or maybe 10 of my vassals are inside my realm but the other 9 are outside my realm.

Basic question: why doesn't my vassal limit match my ledger?

Advanced question: My character portrait has a "realm tree" button. It displays direct vassals.

Postscript:

The interface for Crusader Kings II is a bit challenging. It is difficult to look at the map and understand which provinces are part of my realm. I would expect to find a tree structure (where I can see multiple levels and controlled provinces). In fact, it seems I have to select all my vassals in turn and try to locate their holdings on the map. (It seems I can only see the controlled provinces for one duke at a time. I would prefer to be able to see all the provinces in my realm, color-coded according to duke.)

I know that I can click on a province to get information about it. However, that tends to lead me astray into confusing connections. The realm map (activated by the lower-right-hand menu set) often uses almost exactly the same color for my country and its enemies.