What kind of differences do you mean? R-Type I has the first 4 levels and R-Type II holds the last 4 ones(or are there only 3?). To get all levels in one game, you'll have to purchase the SCD "R-Type Complete".
As far as I know the reason why the game was splitted up, was that the memory of the Hu-card wasn't sufficient for holding all levels. As R-Type was released quite early in PCE's history, they had this technical limitation.