What's the difference between identical(x, y) and isTRUE(all.equal(x, y))?

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Is there any difference between testing isTRUE(all.equal(x, y)) and identical(x, y)?

The help page says:

Don't use 'all.equal' directly in 'if' expressions — either use 'isTRUE(all.equal(....))' or 'identical' if appropriate.

but that "if appropriate" leaves me in doubt. How do I decide which of the two is appropriate?

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