First thing first:
Ideal voltage source acts as a short circuit and sets voltage across its terminals. It is a mathematical construct that does not exist in real life. Its operation does not depend on current flowing through it.
Ideal current source acts as an open circuit and sets current flowing through its terminals. It is a mathematical construct that does not exist in real life. It's operation does not depend on voltage across its terminals.
Keeping that in mind, let's analyze picture one. Here we have two points, a and b, that are connected together. The voltage sources are here in parallel, meaning that one voltage source sets voltage of 10 V between a and b and the other sets voltage of 5 V between a and b. Here our mathematical model breaks down, since the voltage cannot at the same time be both 5 V and 10 V.
My advice here is not to think too much about current or anything else. As I mentioned before, ideal voltage source is there to help with modeling of a real-life circuit and in this case, the model breaks down. If you had say two batteries with shown voltages connected like that, you'd need more components to represent what is happening in real life.
Let's take a look at image 2. We have a simple circuit with a current source. Current source acts as a open circuit, so the voltage sources shown are not connected in parallel. Instead, the sources are connected in series. This way, the model doesn't break down, because we can have any voltage across the terminals of a current source and the voltage doesn't affect its operation.