Real Contractions? 40 Weeks

Rae

I've had two pretty painful contractions with pain starting in my back and radiating to the front lower stomach and my stomach tightened both times. But before, in-between, and after those two, I've had what felt like Braxton Hicks contractions; just tightening of the stomach and no pain. Is it normal to have Braxton Hicks like contractions between painful ones?

Second baby, first time experiencing labor!! Thank you!!