for example, before i got myself a sound card i used the realtek card that was on my motherboard, it had a sound manager that would allow me to separate front jack input/output from the ones on the rear of the PC, so that i could play two different files and hear to two different songs at same time from two different headphones
the realtek audio manager was with the mobo drivers on a CD, dunno if it's possible to download it separately and if it works with other realtek hardware....
in this case a wireless device makes you choose only one playback device, as soon the BT headphones are on, it will switch to those
the sound card does no such thing, front and rear are connected and i didn't found any way to separate them, and if i plug in both headphones, one in front one in rear, both play same file
on top of that there is no notification that something has been unplugged
(talking about Sound Blaster Z sound card)
not sure if same happens with wireless headphones, i had once Sony BT headset but the sound quallity was poor and it messed up my audio drivers