What is the difference, if there is, between this two distillation methods? Reading about water vapor distillation, I found two differents approaches:


Direct one
Indirect one.


The first has an arrange like: 



Here the chamber contains water and the plant. It is cooled and as the water vapor flows away it carries the low volatile compound vapor of the plant/vegetable. Both condense and the oils can be obtained.

The vegetal is on the same pot as water.

The second one:



Here the water vapor is generated on a first po (the blue one) and when flowing through the balloon, it carries the oil vapor. I should remark: the vegetal is on a different pot than water.

Question

Do you see any fundamental difference on the process or something related?

It might has to do with the aggregation state of the material we need to extract, but I'm not sure.
There is no fundamental difference between the two methods. 
In both cases steam is formed and it is passed through the plant material. 
The intention is to extract the non volatile water insoluble essential oils from the plant. 
The method is called steam distillation. 

On the other hand, normally it is not done in this way. 
Since generally only the essential oil is of interest, the integrity of the plant does not matter, it is placed in water and the whole is heated and the water is distilled. 
The students do this in the lab with cinnamon and orange peels, for instance. 
It is much easier because you only have to heat one vessel. 
In these two step setups, you must isolate the part containing the plant very well so that the steam does not condense, once the whole system is hot enough. 
Preferably, you should also heat the part containing the plant, especially in your second example.