This question comes from How can I tell if my installed Android version, not CPU, is a 64 bit or 32 bit one?

On desktop computers it is possible to install a 32-bit operating system on a 64-bit hardware device i.e. you can install Ubuntu Linux 32-bit on an AMD FX(tm)-9370 Eight-Core Processor (64-bit).

Does the same case happens for Android? Is there a 32-bit and a 64-bit version for the same 64-bit device?