I have never seen “Euler circles” used in this context.

It is well known that the nineteenth century English mathematician Venn used circles to illustrate the validity of certain syllogisms.

Your first problem corresponds to the first diagram below.

The A & B circles do not intersect: No A is B.

The x in both A & C indicates existence: Some C is A.

Having diagramed the two hypotheses, we can see that the conclusion is also diagramed: Some C is not B.

On the other hand, the second diagram shows that the argument in the second problem is not valid. The two hypotheses could conceivably be diagramed in a way that the conclusion need not follow.

BTW: Where did you get the term Euler circles?