RF Power Meter vs RF Power Sensor
I think there is no well-defined difference, and it depends on context. 
I get the impression you are referring to a lab-instrument type of meter/sensor and my answer will be along that line:

The power meter is the big box with the screen. The sensor is the little box that you connect to the DUT.

The meter: 
These often have a 'calibration' output that generates a precisely leveled CW tone to 'zero' the error of the power sensor. The power meter will also do a lot of the math to flatten the frequency response of the sensor. Older power sensors came with a piece of paper containing the calibration coefficients: a bunch of numbers you had to plug in to the meter. You also had to set the frequency you are measuring (the sensor couldn't tell) and the power meter would use that to figure out what calibration constants to use. 

The power sensor is the little box that you actually connect to the reference plane you want to measure. It usually operates based on thermal or diode sensors (both have advantages and disadvantages). I believe (historically) these sensors were just that - an analog sensor that generated output signals based on the input power. 

Modern sensors will contain some basic digital circuitry to communicate the calibration constants to the meter, to speed up the process.
On the meter side, I'm starting to see the calibration port being omitted on more modern meters. I'm no expert on the state-of-the-art power-sensor design, but I suspect the stability of modern sensors is simply such that they don't need constant re-calibration. 

Finally, you do get fully integrated sensors/meters now. I think all of R&amp;S's NRPxx series of power sensors can just be connected to a computer with a USB cable, or (if you have the LAN version) you can hook them up to ethernet. In both cases you can just talk to them like any other VISA instrument. You can also stick them into a NRP2 or other power meter box, but in this case I think they just operate as a screen. (kinda expensive screen, if you ask me...)

There are also frequency-selective sensors, which have a narrow bandwidth. This can give you much more accurate measurements for narrowband, low-power signals.