"The relationship is bad."
Translation:Das Verhältnis ist schlecht.
[das Verhältnis] is affair, relationship, love affair, sth between people in emotional way. [die Beziehung] is the contact, relation, more like the type of connection between people.
Was ist deine Beziezung mit ihm? What is your connection with him (like how do you know him)?
But both are used for relationships (like relationship of a couple)