Heather,
My Bob had a vet appointment today and while there, I showed her the picture you posted. Of course, she can't make a diagnosis based on that, but she did ask me a couple questions that I wasn't sure how to answer.
How old is Jinx?
Is any part of that picture a mammary gland?
Is there any other area on his belly with the same issue?
What she did say was -
It could be cancer, but impossible for her to tell.
As a rule, if there is a "mass" on a cat, it needs to be removed. Apparently the percentage chance that a cat mass is benign is much lower than say if it were on a dog. The decision to have or not have surgery would have to be made by you of course, but part of that decision would depend on Jinx's age and current health status (like how safe it would be to put him under anesthesia for instance).
If he is chewing on it or licking it a lot, then chances are it is either extremely itchy, or very painful, and either way, he's trying to make it "go away". For instance, if he had severed pain in his abdomen from pancreatitis, he could be trying to tell you that he's got extreme pain on the inside, and he can't make it go away from the outside, but he sure is going to keep trying.
As far as the bloody/red stool, she said that it would depend on color basically. She told me (and I've seen this at home), sometimes there are bright red drops and mucus, but that could indicate something as simple as tapeworms.
Or it could be very red, or very dark with the red only evident on the "inside" parts of the stool. The cause could range from iritated bowl, infection, or a problem along the intestinal or digestive track. The "darker" the stool, the further along in the digestive process the stool was when whatever is causing the "red" to be present. Any organ involved in digestion could be the problem. Like someone else posted in your other thread, bright red on the outside is probably due to bleeding in the colon area.
I know that most of that information is very "not-definite", but I don't imagine it's easy to make a diagnosis accurately based on just a photo knowing very little about Jinx and his history. I thought I would pass it along anyway, in hopes that maybe something she said will make sense to your vet.
Hope Jinx is feeling better soon,
Carl in SC