The Difference between the Second, Fourth, and Seventh Cases

One key factor is in the usage of the particles themselves:

However, the usual way to distinguish between them is in terms of their different functions:

Second and Fourth: distinguishing indirect object (བྱ་བའི་ཡུལ།) and objective/purpose (ཆེད་དུ་བྱ་བ།)
Second and Seventh: distinguishing indirect object (བྱ་བའི་ཡུལ།) and location/time (རྟེན་གནས། ཚེ་སྐབས།)
Fourth and Seventh: distinguishing objective/purpose (ཆེད་དུ་བྱ་བ།) and location (རྟེན་གནས། ཚེ་སྐབས།)

Due to the idea of directionality, the indirect object is discussed mainly in terms of destination in this context.

Example 1: “Going to the market to buy tsampa.” ཁྲོམ་ལ་རྩམ་པ་ཉོ་རུ་འགྲོ།

In this example:

The Second Case is marking the destination of going འགྲོ་ཡུལ།
The Fourth Case is marking the purpose of going འགྲོ་བའི་ཆེད་དུ་བྱ་བ། / འགྲོ་བའི་དགོས་པ།

Example 2:

Now, the market is no longer the destination for the verb, but rather the location for it. Because:

When we say “Going to the market.”
The action (going) does not occur at the market, once we reach the market the going stops, that action has been brought to its culmination by reaching its destination; in fact, that particular instance of going can occur anywhere else but the market!
Therefore, it is a Second Case marking the destination of going (འགྲོ་ཡུལ།)
When we say “Buying tsampa in the market.”
The market becomes the place of activity rather than the destination; the market is the location where the action of buying is occurring.
Therefore, it is a Seventh Case marking the place of activity of buying (ཉོ་ས།)

Example 3:

With a Seventh Case Time-marker it is easier to distinguish, but the same reasoning applies:

Example 4:

“Bringing water for the field.” ཞིང་ལ་ཆུ་འདྲེན།
“Bringing water in order for barley to grow in the field.” ཞིང་ལ་ནས་སྐྱེ་བའི་ཆེད་དུ་ཆུ་འདྲེན།
“Bringing water to the field in order for barley to grow.” ནས་སྐྱེ་བའི་ཆེད་དུ་ཆུ་ཞིང་ལ་འདྲེན།

In this example:

Initially, the field is marked in the Fourth Case as the purpose of bringing (འདྲེན་པའི་ཆེད་དུ་བྱ་བ།)
Then, the Ladon marking the field goes from a Fourth Case to a Seventh when the sentence is restructured. This is because it is no longer directly linked with the action of bringing (འདྲེན་པ།), but rather with the action of growing (སྐྱེ་བ།).
In this new context, the field is not the destination of growing (འདྲེན་ཡུལ།), nor is it the purpose of growing སྐྱེ་བའི་ཆེད་དུ་བྱ་བ།), but rather it is the location of the growing (སྐྱེ་ས།) and is marked in the Seventh Case.
Alternatively, the Ladon marking the field could be made to link with the action of bringing by being placed outside of the phrase relating to the purpose of growing. It then becomes the destination of bringing (འདྲེན་ཡུལ།) and is marked in the Second Case.