In my experience, the 'Headset' option has terrible sound, and seems to be for use with making calls, presumably when connected with a cell phone. On a related note, right above 'Headphones' on your list is a 'Headset' option, with the subtitle (or whatever it's called) 'Ink'd Wireless Hands-Free.' I have pretty much the same option on my computer, and it seems to be a second connection for your headphones, but they both can't work at the same time. Under the 'Playback' tab of your Sound window (which you have provided a screenshot of), right-click on 'Headphones' (Ink'd Wireless Stereo) and select 'Connect.' I'd probably also set it as your default device, if it isn't already.
Turn your headphones off then back on (using the power button on your headphones, probably by pressing and holding until they make a noise), this could automatically reconnect them properly.
There are a couple things that you can try:
I sometimes have a similar problem with my Beats Wireless Bluetooth headphones.
