You don't need me or anyone else to tell you that you're free to call it whatever you want.
I'm going to keep referring to the QuickSync video encoding block in my CPU as "hardware," though, because the tiny lump of transistors that is dedicated to performing this specialized task is something that I can kick.
Relatedly, the business of managing raw NAND storage on Apple devices and abstracting it to operating system software as NVMe: That translation happens in hardware. That hardware is also something that I can kick, so I'm going to keep calling it "hardware".
QuickSync isn't analog to an SSD controller. One is a specialized IP block that handles video streams, other is a generic ARM or RISC core running a specific software for handling low level NAND operations.