What is "reconstituted" milk? Here in Chile nearly all milk you can buy in supermarkets is UHT milk in tetra bricks. Some brands state on the carton that the milk is "reconstituted", while others state that it is "not reconstituted".

What is the difference between the two? Are they processed differently? What part of the milk does the "reconstituted" refer to? And would it make any difference using one or the other in the kitchen?

If I remember correctly the "not reconstituted" milk is usually a little bit more expensive. The taste to me seems to be the same (I didn't do any side-by-side comparison though).
It's the equivalent of 'from concentrate' on fruit juices.  Only in this case, it's made from dry milk powder.