Yeah, there are different bluetooth audio profiles, one for high quality audio intended for media consumption, and one for bi-directional audio intended for telephony (and some others, but these are the relevant ones here). The “gotcha” is that in general, any attempt to consume the mic feed from a bluetooth headset will switch it to the telephony mode, so if you have them paired to a PC and an application is listening to the mic for any purpose you get stuck with much lower quality 64kbps PCM audio.