What is the difference between a mat and an far infrared sauna? Are there benefits over an infrared sauna?

Though both the mat and sauna have a lot in common regarding FIR rays emission, there is also some difference. 

Infrared Saunas work so that electric heating pre-heat black carbon panels and these panels transform conductive heating energy into radiant heat or FIR rays. In Amethyst Mat, the same process is done by amethyst crystals or a blend of several gems. 

Crystals rays are deeper penetrative, but they have most of the heating energy concentrated around 5-7 and 12-15 microns, so-called Amethyst peaks wavelength. It may have some bio resonant effect on micro-level molecular vibrations increasing heating by our own cell energy stations (mitochondria) stimulation. 

Hot crystals also generate negative ions creating a refreshing environment similar to lush forests, ocean beaches, or waterfalls. Even the large single-size mat (also best for sleeping) is rather compact than the sauna and now is less expensive.