For many years now, we have always use the term "hardware" firewall to include only firewalls that used a flash ROM or read only RAM drive type of media to store OS and config information.
Every other firewall were "software" firewalls. The distinction for us is we never wanted an entire network to be down due to HDD issues. Back in the day, ROM was just so much more reliable than HDD media. The tables have turned as HDD is getting so cheap, it is now easy and affordable to create redundant drive setups for those "software" firewalls.

I think any more it's a matter of semantics pure and simple. Don't you think?