The difference between PC-based oscilloscopes (referred to as a USB oscilloscope) and stand-alone oscilloscopes is that a USB oscilloscope does not have buttons or a screen and is connected to a computer through a USB. The device is then controlled by the computer and the results are displayed on the computer screen.
The Red Pitaya board certainly falls under the PC-based oscilloscopes and might be categorised as USB scope even if the interface used for control and data communication is Ethernet or WiFi and not exactly USB. This is just because of the large use of USB oscilloscope term but not of terms like Ethernet oscilloscope or Wifi oscilloscope. Similar situation would be calling a copy machine a xerox machine; a lot of people will refer to it as a xerox machine even if it is made by a different manufacturer.
At the same time a Red Pitaya board can turn into any of the popular instruments like: Digital Logic Analyzer, LCR meter, Vector Network Analyzer, Spectrum Analyzer, Bode Analyzer or Signal Generator and so on, thanks to the ability to go to the web marketplace and download apps that have been developed by the company that created it and even by other users.