Think of Braxton-Hicks the way the Dutch do--"hard belly contrax". That is, they are mainly felt as a hardening of the whole belly/uterus--but not felt in the cervix so there is little to no pressure or pain down low and center, little by way of lower back sensation. These are true Braxton Hicks, and are simply toning contrax that help get the uterus ready for the work of labor. They generally do increase in frequency and strength as pregnancy progresses--but still are going to have an impact on the cervix.
Prodromal labor can also be called 'labor by installments'--they are 'real' contrax, felt in the same way as labor though they may be milder and shorter in duration and farther apart. But this kind of labor may well have contrax that are just as strong, just as frequent, as real labor....it's just that these contrax will stop before baby comes. This kind of labor does effect the cervix to some degree (perhaps not a lot--and sometimes, producing quite a lot of effacement and dilation over time).
Some women have days/weeks of prodromal labor--or bouts of it, a few times a week--and do go on to have speedy deliveries. Unfortunately, having prodromal labor, no matter how often or strong, does not necessarily equate with 'speedy delivery'. It often does, if the prodromal contrax have indeed brought effacement and dilation, and good positioning of baby...but there is no way of knowing for sure in advance.