Do feet feel warmer on a rug than a tile floor because the rug

They actually are not different at all, but only feel like they are different temperatures because the tile floor is a better heat conductor than the rug.  Since your feet are  warmer then the floor the tile floor conducts heat away from your body faster than the rug, so your feet feel cold

There are both the same, the temperature from your body just makes it seem different I believe.