I could be splitting hairs, but to me, guilt is established by another party, and something you may or may not recognize, whereas shame is mostly sourced internally. Someone, including the government, my employer, and other people, can declare me guilty of something. I also can admit guilt, but its not required. Shame on the other hand is something that only exists if I personally feel it.
I do agree with the notion that this may be somewhere close to one of the major differences between Western and some Asian societies (I'm thinking of Japan primarily, as that is what I have experience with, so this may not extrapolate to other Asian cultures). In Japan, I was shocked at the low crime rates. I could leave my bike unlocked pretty much anywhere and not worry about it being stolen. They leave vending machines on random alleyways everywhere with no fear that someone will break into them. Crime in general is just so much lower, despite opportunity potentially being much higher. Additionally, streets are so much cleaner than American cities. People don't defecate on the sidewalk. They clean up after their animals. Public transportation is clean and reliable and you aren't going to be screamed at by a homeless person. I think a lot of this comes from the fact that Japanese culture has a strong element of shame attached to people who transgress societal rules. In Western countries, the emphasis is more on guilt, which leads more to a culture of "getting away with what I can", and "its only a problem when I get caught". We litter more. We steal more. We are more violent. We tend to put less effort into our jobs.
Of course there are flip sides. I think the strong sense of shame and societal responsibility in cultures like Japan's also leads to more mental health issues, higher suicide rates and societal isolation. Tougher work environments and cultures. Sometimes a stronger apprehension towards challenging the status quo. I'm not sure if one is more ideal than the other. I'm personally a big fan of the societal cohesion that seems to exist in Japanese culture, but I have friends who found it stifling and sterile.
And yes, both emotions are often at the root of street violence.