mat
A mat is a flat pad, or small rug used for a variety of purposes. Some mats serve as a barrier with the floor to be used for floor-based activities, while others serve to collect dirt, or moisture preventing it from getting tracked onto the floor, or other unwanted places. Not all mats are designed to be placed on the floor.
The primary difference between a rug and a mat is mainly size, and that rugs serve a decorative purpose, while mats are designed to be functional. For this reason mats tend to be simpler in design than a rug might be, and come in a wider number of forms.