Exactly. A hotel typically chooses to offer a government rate that matches the GSA lodging per diem rate for the area. Again, it is entirely voluntary on the part of the individual hotel, and occasionally hotels will offer "government" rates that are above per diem (which is a topic for another thread).

Sometimes Gov rates are a good deal and sometimes not. D.C. area hotels are a good example: The Gov rate can be a great deal compared to commercial rates for Monday through Thursday nights, while Gov rates on Friday through Sunday nights are often much higher than commercial rates.