Genealogists try to be specific when stating relationships between individuals. Your relative from Omaha might not be as specific when discussing family members. Grandma may have written “Cousin Myrtle” on the back of a photograph.
If the person referring to their cousin is still alive, try and get them to be more specific about the relationship, if possible. Don’t suggest what the relationship is. Sometimes “cousins” were were actually cousins (just further down the line than you thought), were related by marriage, or were just neighbors with whom the family was close.