What is the difference between iPad and iPhone charger?
They both output a similar voltage level ~5V. However this is going to change once you start drawing current from the charger. The output will decrease if you start pulling more current. 

iPad charger provides 2.1 A at 5.2 V means you can pull 2.1 A and the output will stay at 5.2V. Output voltage might go down if you draw more current (say by attaching 2 ohm resistor across the leads and trying to draw 2.6 A) and thereby also reduce the expected output current.

Similarly, iPhone charger will be able to provide rated voltage (5V) only up to 1A of current draw. After that, you might see a voltage drop.

In terms of hardware, iPad charger will have a higher power circuit - most likely a bigger flyback transformer, mosfets with higher current capacity and bigger filter capacitors. 

You can benefit from ipad charger while charging an iphone if your iphone is able to draw current higher than 1A. If this is not the case, then there is no point. However you will notice longer charge times when you charge your ipad using iphone charger.

Also, it's false assumption that load remains the same. Here is a sample charging current and voltage curve for a li-po battery which I picked from a google image search:



As you can see, initially the battery voltage is lower since it has discharged. Once it starts charging, the voltage increases and the charging current decreases.