Flate rate vs fixed rate plans

I'm moving to Houston and I'm confused about some of the recommendations about electricity plans I have seen. Are flat-rate plans considered the ones that have the same Average Price per kWh for 500 kWh, 1000, and 2000, or are flat-rate plans considered the ones that have a fixed rate for each monthly use for instance 13.2 cents at 500 kWh, 12.7 cents for 1000 kWh, etc? The reason I'm confused is that I see some people recommend plans that are the same average price per kWh across 500 to 2000+ but on powertochoose I do not see plans like those anywhere. If possible can someone clear this up for me?