Look at the prints for booya and kada: they have 0 and 1 preceding them. Why? Because those are the indices in an array.

In the first dump you gave, the container that held a reference to ['booya', 'kada'] had no interesting type of its own, therefore its stringification was REF (ref-to-a-ref). In the second case, you had an array container, and the first element of the array was a reference to ['booya', 'kada']. The second case, with the 0, should be clear: the 0th element of the array pointed to by \@ary is the anonymous array.

In the second case, there is no index, there's just a straight reference. That is signified by an arrow.

I think this is the kind of thing you either don't worry about, or deduce, or read the source for. :-)