zij-ze are the same, so are je-jij. They're all subjects btw. Je can also be a indirect object, jou is an indirect object, so are hun and hen. (hun can also be possessive pronoun). Ze can be both subject and indirect object. It's all about context.
the combinations for subject - possessive pronoun - indirect object are :
ik - mijn - mij/me
jij/je - jouw/je - jou/je
hij - zijn - hem
zij/ze - haar - haar
wij - ons/onze - ons
u - uw - u
jullie - jullie - jullie
zij/ze(plural) - hun - hun/hen/ze
In spoken Dutch you might also hear me instead of mijn, ze instead of zijn. Also some people write Dutch the way they speak it :-)