Ontological model versus Conceptual Model

I wrote for 1 hour 15 minutes this morning

What is the difference between an ontological model and a conceptual model. Wand and Webber argue that there should be a one-to-one correspondence between constructs in the conceptual model and constructs in the ontological model. Why? What is the difference in the purposes of the ontological model as compared to the conceptual model?

The example I am currently struggling with deals with the difference between negative attributes and negative properties. Clearly, an ontological model has no place for negative properties. A thing possesses properties, but the myriad properties that it does not posses represent no property at all. That is, a person has the properties height and weight and may have property called "brain tumor mass" but a person without any brain tumor does not have the property of "not having a brain tumor." From an ontological perspective, this seems to make sense as the existence of negated properties might require an ontological model to state what is not possessed by an individual--an extremely burdensome task.

But Bunge clearly acknowledges the existence of negative attributes (1977, p. 60). Would these be allowed in a conceptual model? What is the trouble with creating a class called "person" that has attributes that all people share in common that also has optional relationships to conditions (such as brain tumor) wherein all required attributes of brain tumors are represented?