My dutch teacher told us that many times, "ze" and "zij" can be used interchangeably but when you want to emphasise to a particular "she", use "zij" and in general, use "ze".
For example - There are 3 girls and someone asks "Who takes eight apples (Wie neemt acht appels)?", you'll point to one girl and say "Zij neemt acht appels"
Then someone asks, "How many apples does she take?". To which you'll say, "Ze neemt acht apples"
Because in the second one, the emphasis is on the number of apples and not the girl/lady!
Hope this clarifies (and hope I'm right, I'm new to Dutch).