A wireless communications device may include a wireless receiver, and an adaptive demodulator coupled to the wireless receiver. The adaptive demodulator is configured to apply first and second bandpass filters to amplitude information of a received signal at first and second frequency bands, respectively, and classify the received signal as one of a PSK modulation type, a second PSK modulation type, and a third FSK modulation type based upon whether a tone exists in the amplitude information of the received signal in one or more of the first and second frequency bands. The adaptive demodulator is configured to adjust a demodulating parameter based upon a classified modulation type of the received signal.