You can definitely feel the difference with braxton hicks. I started getting it at 22 weeks (24weeks today), it's slightly uncomfortable and it's all over the belly, it shouldn't be painful. Each time I have them, my son starts moving about and kicking me afterwards :)
That is just the baby laying on that one side, which causes one side of the belly to feel harder than the other because all of his or her weight is pressing there. With Braxton hicks it's an all over tightening in the belly not just on one side and usually for me it gets a little harder to breathe because of the tightness.