To be honest, I refer to them all as "spectrum analyzers" (well, actually just "spec ans") and pretty much every person I work with on that team also just calls them "spectrum analyzers"
The FAQ on our webpage is how I would make distinction if I had to, but we have several instruments (FPL, FSVR) that can analyze and demodulate vector signals (cellular, Wi-Fi, etc.) but still have "spectrum analyzer" on the label. And our flagship analyzer, the FSW, has "Signal
and Spectrum Analyzer" on the front

So if we use the definition in the FAQ, the FPC would be a spectrum analyzer because it doesn't analyze or demodulate vector signals. That's pretty much all there is to the name.
Incidentally, I have an FPC in my office right now, so please also feel free to ask me any questions you might have. I've already made about a half dozen videos on the FPC (see the R&S YouTube channel) and am working on some new videos this week showing how to use the FPC1500 for network analysis (that model has an integrated tracking generator and VSWR bridge).