Emulation just means running it on hardware it wasn't intended. That runs the spectrum between ISA emulators like Dolphin, software RTL simulators like verilator, and FPGAs can certainly be used for emulation if the design wasn't really intended for them as the real end goal.

There's also an interesting point in that spectrum of the cadence/synopsys hardware emulators. They run in a rack sized device composed of a bunch of FPGAs and arrays of custom ascetic processor cores that can only do logic and branch ops to run HDL for SoC sized designs at ~1-10MHz.