I never see refrigerators being called AC either, and they’re air-to-air heat pumps too. People just call things what they want regardless of the technical details.
The actual technology is called refrigeration. We should really be calling them all refrigerators, including AC, heat pumps, whatever. AC is a specific application of the refrigeration cycle, and so is a heat pump.
Pointless discussion, but they’re all heat pumps. Refrigeration cycle is the name of the physical process. Most heat pumps make use of that thermodynamic principle, but there are some niche ones that don’t. But people don’t care about that, and so find it more useful to call them by what their purpose is, and that varies locally.
Actually that’s wrong. When we build food refrigerators using peltier modules, it’s still a refrigerator. The reverse carnot cycle is just one type of refrigeration cycle, reverse rankine and reverse brayton cycles still count.
Sure you could call them all heat pumps, and you might be technically right. Nobody actually calls them that though. Most people probably haven’t figured out that an AC unit, a heat pump, and a food refrigerator are all actually the same concept in different dressing and sizes.
It’s only an irrelevant topic if you can actually communicate clearly, which is actually very hard as almost no one understands this stuff. Especially in the UK where this is all viewed as newfangled, expensive, and unreliable technology. To be fair they aren’t wrong in this country: the way we handle, specify, and install ASHPs makes them feel and act inferior to a good old condensing gas boiler. It’s a sad state of affairs.