I had very strong, painful BH from 28 weeks with both pregnancies. Baby engaged early both times aswell. There is very little information out there about painful BH. Most mws also will tell you that they shouldn't be painful. Mine were, both times. Not enough to be in agony but enough to cause me to take paracetamol and get in the bath. Mine would also last several hours, getting closer together etc mimicking labour.
The way you can tell they are BH is the following - they won't last longer than 40 seconds at most, per contraction. They won't be felt in your back whereas a lot of labour contractions are felt in your back and very low down. They may last over several hours but they won't be regimented - you may find the following pattern for BH: 20mins apart (x4), 15mins apart (x3), 17mins apart (x2), 3mins apart (x10), 5mins apart (x4) etc.
Labour contractions, including early labour, will be far more gradual and you will not jump from close together to far apart to closer again. Don't get me wrong, you may have a few that come two together or a brief gap when in labour but it won't constantly jump about like above. The rule of thump I was told was that labour will obviously become more and more painful until you can't talk through them. BH won't. So if they are regular for 4-5 hours, becoming increasingly painful and lasting 45seconds - a minute you may need to check you have your bag packed! Otherwise, it's BH.
If it helps, both my labours were quick and fairly easy. Im sure all that contracting in the weeks leading up helped.