You're right that the logical structure is similar, but the term "circular logic" is when a circular causal relationship is stated, like "A caused B and B caused A", which is often a logical fallacy but can be valid in feedback loops where a repetitious sequence of phenomena is self perpetuating to some degree and may be initiated at any point in the circle.

An example of this is the oppressor-victim-savior triangle that plays out in matters of law. Possibly oppression initiates such a sequence, or someone may claim victimhood falsely, initiating a savior to appear who then oppresses the falsely accused who must then save themselves with exculpatory evidence and may retaliate.