In the academic sense, an annuity is payable annually for a term of years and a perpetuity is payable annually forever. An annuity has an end date and a perpetuity does not.
Many commonly seen annuities are structured to pay until death of the recipient, which for the issuer can be averaged and anticipated using actuarial tables (i.e. the anticipated average number of years for the aggregate is known, even though individual payees may live longer or shorter lives). This is still analyzed as an annuity for a term of years.
An annuity may be payable upon retirement, but there's no financial reason you couldn't delay a perpetuity by a term of years. You'd value it as a perpetuity, but discount it for the future value based on the retirement date. I don't believe anybody does this currently. You could also index a perpetuity, but of course that would raise its cost to purchase at the front end.
Tax treatment of annuities can be favorable to the extent that insurance rules are more favorable than one might expect. But the payment of interest is generally ordinary income under IRC §61, whether it is payable every year or for a term of years.
The last difference you list is the actual rule. Perpetuities are payable forever, so do not cease with death. An annuity that ceases with death is payable only for a term of years (even though the term may not be known ahead of time for any individual annuitant). A perpetuity continues paying, so it's just a stream of income. Of course, perpetuities could be called back by the issuer in exchange for some value (possibly a cash settlement sum or determined by a formula), which terminates the perpetuity obligation. But the mathematical valuation is still based on the idea of endless payment.