The difference is how the output is specified.
The "Area" tool will generate solar radiation estimates for each grid cell of your input DEM.
The "Point" too will generate the same solar radiation estimates, however, a point file is required in as an input parameter along with the DEM. This point file represents your points of interest. So, if you only care about solar radiation estimates for a set of point locations within an area, then this tool will run faster than the area tool and the output solar radiation values will be attributed to the input point file. No raster surface of solar radiation is produced.
If you run the "Area" tool and then run "Extract Values to Points" you will end up with the same output as if you had run the "Point" solar tool.
Basically, if you need the full solar radiation surface as a grid, then run the "Area" tool. If you only need the solar radiation for a specified set of points, then run the "Point" tool.
Hope that helps.