BH can be very painful sometimes, in my last pregnancy they were usually more painful than my early labor contractions. BH, however, do not contract the entire uterus. Labor contractions start at the bottom of your uterus and spread up tensing the entire uterus. My experience with BH they usually started on the side moving forward, but always left a soft spot at the top. BH are irregular, but may continue for a long time. If they last more than an hour contact your doctor.
Between 36-37 weeks I went to the hospital because I had contractions 5 mins apart. Didn't dilate but they stopped them with a shot. The hospital said they were real, but it's the only thing I have to go on, so no idea about BH. I've read and doctor has confirmed that regular timing and pain that starts in the back is likely real. Just the tightening and contracting at irregular intervals is BH, feels like a contraction, but they're likely just annoying and painful and not causing dilation or effacing. Once you're over 37 weeks, they won't stop them though. They just let the baby pop out at that point. Good luck!
When the pain is random and can't be timed it's braxton hicks. When the pain is so intense that you can barely talk and it can be timed that's the real deal.