Typically, the diode detector measures voltage which can be used to calculate power.
The power sensor measures thermal energy and gives a true representation of power.
Randy
Since most power sensors have a 50 ohm input impedance, if you measure the voltage then you know the power.
Many power sensors are in fact diode detectors. When operated in the square-law region, the detector's output voltage is proportional to the power.
If you look at Keysight's power sensors, they have two types: most are diode detectors; the other is thermistor or thermocouple based. The thermistor power sensors use a thermistor to measure power by measuring the temperature rise with a thermistor. Similarly with thermocouple sensors.
Lately, with cell phones and LTE, there is a lot of interest in measuring signals with multiple carriers that have a high peak to average power ratio. So you get two different types of power measurement: peak power and average power. Thermistor sensors only measure average power. Again if you look at Keysight's sensors, they have some that can measure both peak and average power. This requires diode sensors.
Here's Keysight's power meters and sensors for reference:
http://www.keysight.com/en/pc-1000000475%3Aepsg%3Apgr/power-meters-power-sensors?cc=US&lc=eng