I want to know the orthodox answer in relation to Biblical Judaism and not modern unorthodox Judaism sects
Lev 19:34 is about strangers. Are converts "strangers"?
The Jewish tradition distinguishes between a Proselyte who lives among the Jewish ("?? ????") and a true Proselyte who bocomes a Jewish person.
Becoming a true Proselyte is a long and hard process, because Judaism doesn't readily accepts newcomers to its ranks. You have to prove that you truly want to become Jewish, and learn a lot about the religious and traditional aspects of Judaism.
A true Proselyte is both a Proselyte ("Ger - ??" in Hebrew) and Jewish. A proselytes is Jewish, just like any other Jewish person, and the bible as well as Chazal ("the jewish elders of ages past") have a very positive attitude towards them, and they warn people against discriminating or harming them.
Shaiel was right on. Some people chose to live among the Jews, and worship the same G-d, and follow the 7 Noahide laws. Not everyone would become Jewish...this if for many reason. For one, it isn't necessary to become Jewish to be considered a righteous person. Non Jews have 7 laws to follow, Jews have 613. With that said, when some does convert, they are not considered converts, and it is considered inappropriate to bring it up, or to ask questions about their old lives. Assuming someone completes an orthodox conversion they are considered Jewish in every way.