There is Hardware, Software, Firmware and ...FPGAware?
In a project, engineers typically call a functional unit by its function. If they have a baseband processor in programmable logic, they will call it "the baseband". Likewise for modems, rf frontends, crypto-cores, network processors etc. Firmware is by no way "firm" in the development process. Exactly this is what makes programmable logic so attractive for development.

The software vs firmware vs hardware distinction is more about how easily a unit can be replaced in the field. Since FPGA-bitstreams are often stored together with other firmware in non-volatile memory, its OK to also call it firmware ... since the process to update it is the same from a user perspective.