To me at least, BH feel more like you're doing crunches. Everything gets really tight, then releases. I have been told the cramping is more like real contractions, not BH.
BH is like a painless tightening that makes my belly really hard. Real contractions were painful (though mildly at first) and felt like waves moving around the belt region.
Cramps can be early labor. I've had what feels like mild menstrual cramps for weeks. You might also be feeling just a general stretching of that whole region as it gets ready!