what is the difference between voltage output swing at no load vs at 10k load?
A rail-to-rail output amplifier is designed to swing very close to the supply rails, unlike older op amps which sometimes couldn't get closer than a few volts.

However, there is a finite output resistance in the output stage, meaning you can't swing exactly to the rails.  As the output stage starts to deliver current to a load the voltage drop across the output devices has to increase.  

What the datasheet is saying is that with a 10K resistor between the output and ground, you are guaranteed to get within the specified voltage of the voltage rail on the output before saturating or clipping.

Lower resistance will result in a higher drop.