The name 32C comes from the 32C hardware that it emulates.

It emulates... because... it is software. Yes, this is about a softwar
product. Mixbus 32C is a software product, based on Ardour. As the
subject line states. Just making sure everyone is one the same page.

Harrison has been mostly in the business of making digital consoles for a couple decades now.

The previous product with the Mixbus name used the EQ, dynamics, and tape saturation algorithms from those consoles, thus literally providing the same channel strip. Not an emulation, the same thing. At least that is what Harrison claimed.

So yes, the distinction matters.