"Rabbinic" Judaism and "Regular" Judaism, what are the main differences between the two?

there is some misunderstanding. the regular i.e. dominant form of judaism now and for many centuries past has been rabbinic. practically all jews are rabbinic jews. there is a tiny number of karaite jews who are not rabbinic. the difference in theory anyway is that the rabbinic jews accept the idea that in addition to the written law (torah) there is an equally valid oral law, which for many centuries was forbidden to be written down and eventually was set down in the talmud--whereas the karaites do not accept this. it is commonly thought that the rabbinic jews are direct descendants of the pharisees mentioned in the NT (this was before the oral law was written down of course). of course, like all human religions and ideologies, it is all partly eyewash. the advocates of the oral law as we have seen ended up writing it down, and those who reject it of course have their own interpretations of the torah which in effect constitute their own oral law (and in some cases are less literal in their interpretations that rabbinic jews). anyway rabbinic is regular simply because the karaites refused to accept converts or to intermarry and so gradually their population shrank, whereas rabbinic jews have done both for centuries and have become far more numerous. there are also samaritans, who are not considered jews at all, but are closely related, who also do not accept the talmud and whose torah is slightly different and who preserve many of the ancient traditions like animal sacrifices and the original hebrew alphabet (the jews use the aramaic alphabet).