Truth and senses in "The Tell-Tale Heart" and "The Black Cat"

While reading "The Tell-Tale Heart" and "The Black Cat" one after the other I found interesting similarities and differences between the two. In the first story mentioned, the tale begins with the word "True (555)" and throughout the entire text Poe is pushing the notion that the story is true and that the narrator is not mad. It is also stated that "the disease had sharpened my senses (555)" which is interesting. What disease? The eye itself or did it physically do something to our narrator?

In the next story the narrator states "I neither expect nor solicit belief (597)" which is opposite the view of the first. However, this narrator, like the first, does not want us to think he is mad but brings in his senses in a different way; he says, "Mad indeed would I be to expect it, in a case where my very senses reject their own evidence. Yet, mad am I not (597)."

I wanted to bring up these points in hope that someone else may have seen another connection that I missed between the two stories. What do you think Poe is trying to say here? Perhaps something about the uncertainty of verbal stories. Maybe if the stories were written down they would be more believable but since they are coming straight from the mouth's of the criminals/"madmen" the reader/listener should suddenly be wary of the truth? Also, what do you guys think about the senses that Poe brings up in both stories?