Logic is a discipline that studies a. the psychological processes involved in reasoning, b. the relations between beliefs that are the outcomes of reasoning, and c. the brain processes involved in reasoning.
An inference is a relation that obtains among beliefs if and only if a. they are all true, or b. they have the same content, or c. one of them is supposed to follow from the other or others.
Whenever beliefs that are logically unrelated are said to be an inference, this is a. a failed inference, b. a strong inference, or c. a weak inference.