The image from Apple's Documentation describes it very well:
Array
is an ordered (order is maintained when you add) sequence of elements
[array addObject:@1];
[array addObject:@2];
[array addObject:@3];
[array addObject:@4];
[array addObject:@6];
[array addObject:@4];
[array addObject:@1];
[array addObject:@2];
[1, 2, 3, 4, 6, 4, 1, 2]
Set
is a distinct (no duplicates), unordered list of elements
[set addObject:@1];
[set addObject:@2];
[set addObject:@3];
[set addObject:@4];
[set addObject:@6];
[set addObject:@4];
[set addObject:@1];
[set addObject:@2];
[1, 2, 6, 4, 3]