They were regarded as one. During the time when thete were two emperrors (Rome and New Rome/Constantinople) if one law as enacted in the Eastern part the law was valid in the Western part, also viceversa. The Eastern part was economically and culuturaly more advance and that was the biggest difference.

At one point the Eastern part was unable ti defend the Western part, other than Justinian who tried to unite them again. Unfortunately it didn't last too long.