Hello Many questions,
Welcome to HealingWell!
You've come to a great place... Hopefully we can all help each other.
No, IBS does not always present with a specific pain in the exact same spot. BUT, that's not to say it can't for you. The thing with IBS is that it is a diagnosis of exclusion. If the docs can't find an explanation for your woes, then you have IBS. I usually get lower abdominal cramps that go away after I use the restroom, however, occasionally I get what I think are gas pains that hit me all the way from my breast bone to right above my pubic bone.
I would think that with Diverticulosis the pain would be more consistent. But, I don't have it so I don't know. IBD might be a little trickier because Crohn's, for example, can show up anywhere from your mouth to your anus; it can probably make your entire body hurt. Ulcerative Colitis is more specific to the colon and rectum. The pain might be in a smaller area but still maybe not in the same spot as ulcers reappear randomly.
How bad and how often is your pain? Do you have daily D? Did your doc prescribe anything, like an antispasmodic?