The distinction between the terms "firmware" and "software" can be somewhat vague.
Some can apply the term "firmware" to software that is used mostly internally, without visible change or interaction with the user. For example, the firmware in a graphics card. In this case, "software" would be used to refer to "programs" you install, but which are not necessarily "fixed".
Accepting this distinction, built in software in an embedded system would be aptly called "firmware". But there is one more twist. Not all that firmware is necessarily a part of software, as some equipment's firmware can include changes to FPGA's configuration, which is equivalent to a hardware change.
So, in embedded systems. Can you choose which software you install in your transceiver? You don't, so it's called firmware. And, as I said, that firmware can both include actual software and FPGA configuration.
However, if you have one of those SDRs that work by running software in your computer, at least in theory you can use different SDR programs with the SDR transceiver, so it's "software". However, the SDR box will probably have firmware as well (the basic part needed for communication with the computer and, again, whatever FPGA configuration it includes).
It's somewhat different if you have one of those oscilloscopes based on Windows and you install, for example, Matlab. That would be called software, not firmware.