Colt incorporated the USMC recommended changes, etc., etc., and developed what became the M16A2.
One of the changes meant that the M16A2 didn't have an AUTO setting, only BURST.
The Navy wanted some of the new guns, but they wanted AUTO capability.
Some guns were made for for the Navy -Voila! M16A3. FN got the contract - Colt never made any M16A3s.
(Apparently Sabre Defense has recently also gotten a contract for A3 production. But not Colt.)
Meanwhile, an A2 with a flat-top receiver was being developed. The successful prototype became the M16A2E1.
The M16A2E1 was adopted, hooray! But the M16A3 designator was already taken by the Navy.
So, the Army adopted the M16A2E1 as the (drumroll) M16A4.
The End.
Epilogue: The flat-top receiver was a Good Thing, and inevitably has been finding its way onto some of the Navy's A3s. But they weren't born that way.