We believe both kitties have homes. The tabby may be from two houses down and the big fluffy gray kitty might live on the next street over. At least they eat well here and we have two cat houses set up with blankets inside underneath our porch just in case. The gray cat doesn't show up that often.
The reason we still put food out is for Bijou, the black kitty we TNR'd over the summer. She shows up a lot.