How to refer to a noun that has been introduced using "another"?

The language here is consistent with writing about sets. For example “oranges and pears constitute a set of fruits, “oranges and lemons constitute another set of fruits”.

The first set is a mixed fruit set; the second is a citrus set. If for some reason (you omit to say why. Perhaps you could edit to explain this?) you cannot refer to first and second set, you might say “These sets of fruits are different).

In set terminology, these two sets of fruits are different (one containing B, the other B1) but they are not entirely separated (having A in common): they intersect.