Some METAR reports are not especially helpful for discriminating between the two different sea level pressures, either. Sea level pressure in a decoded METAR report would indicate SLP as “SLP (sea level pressure).” But for Altimeter (setting), there is no equivalent descriptor and no indication that it is, equally, a sea level pressure just like SLP.
It seems some (most?) weather station manufacturers are avoiding using the standard meteorological terms like station pressure, Altimeter (setting) or SLP.
Unless I'm missing what you're getting at, the altimeter in an encoded METAR is notated by an "A" followed by the setting, minus the decimal in inHg, but I know you must know that. As far as the equivalent descriptor, my take is that the people who primarily use this information have been educated on the similarities and differences of the two, and most novices don't care, unless they're "us".
Like I said in another post, things continue to be dumbed down for the buyer, hence the lack of description. At least the VP2 and Vue console tell you what you're choosing, and that's the way it should be, even if there is no choice. Which is it? Temp is temp, humidity is humidly, but the pressure is not necessarily the pressure, if you get my drift. Exactly why the type of reduction (or none) being used should be included, always. That irked me about the 6313, they tell you nothing.