Equal sets are those sets who have the same elements and same cardinality. For example:
they are equal sets because they have the same cardinality and same elements.
Equivalent sets are those who have only the same cardinality. For example:
We can say that they are equivalent sets because they have the same cardinality.
All in all, equal sets needs to know the cardinality and elements of a set while in equivalent sets, only cardinality matters