The Download page mentioned that only the ISO has the option to install to a HDD or SSD.
You are misinterpreting this. What it means is that once booted and running, the ISO version is capable of creating an install to a HDD or SSD.
It has always been possible to write the generic-pc-serial and generic-pc versions to HDD, SSD, or CF card, but you must use a third party tool to do do.