When it comes to deep comparisons, I would define "equivalent" as being equal by value, and "identical" as sharing the identity.

In my experience, it's RARELY useful to compare things as being identical beyond the top level scalar. It's COMMONLY useful to compare things as being equivalent to all depths.

And lastly, if you like checking if things are identical, then you'll probably love seeing if things are equivalent to a certain depth, and identical below that depth. For example, { $x } is not identical to { $x }, because the curly braces produce two equivalent hashrefs with identical contents.