To answer the most important question: No, switching from yellow to green will not in any way harm your engine. However, the dealer did not do you a good turn by doing this - they used a less expensive coolant than the one that originally came in your truck.
First of all the colour of a coolant is simply a dye added by the maker to indicate whatever it is they want to indicate. That being said there are some general industry customs that most follow.
Green colour coolant in the USA is the old standard non-long-life coolant that has been used successfully for many years. It protects the engine very well and has only one issue - it must be replaced every 2 or 3 years or every 30,000 to 45,000 miles as the anti-corrosion additives are used up. As most consumers didn't follow this replacement regime, engines cooling systems had issues with corrosion - not because anything was wrong with the green coloured coolant, but because it simply needs to be periodically replaced.
Ford switched somewhere late in the 2002 Explorer model year to yellow coloured long life coolant. This coolant uses a different set of anti-corrosion chemicals and this allows the coolant to be used for 5 years/150,000 miles before needing replacement. Basically it makes antifreeze into a lifetime fluid for consumers who get rid of their cars before 5 years of ownership.
The yellow coloured coolant doesn't protect any better against corrosion than the green coloured coolant, it simply lasts longer.
Your 2003 Explorer originally came with yellow coloured coolant from the factory.
In order to work on a coolant system it is necessary to drain the system so coolant doesn't pour all over ones face while removing hoses and parts and the like. The dealership *should* have refilled your explorer with the yellow coloured coolant as it came with that originally. Instead they saved themselves a very few dollars and used the non-long-life green coloured fluid.
As a side note, many people will swap out green coloured fluid during a change to yellow coloured fluid to save themselves from having to do it again for a long while. Very few will go from yellow to green willingly. Your dealer did not do the right thing, although in the scheme of things it is not harmful either. The fact that they didn't fix the leak is the issue with the dealer.
Technical stuff:
The green coloured coolant uses Inorganic Acid Technology, or IAT, to maintain it's corrosion protection properties. It is these chemicals that are used up.
The yellow coloured fluid is known as G-05 and uses a Hybrid Organic Acid Technology or HOAT. These chemicals last much longer than the IAT chemicals.
The main constituents of coolant are water and (typically) ethylene glycol which together make up ~95% of the coolant. These two ingredients never, ever wear out. Please do note that ethylene glycol tastes sweet and is wildly poisonous - as little as 5 teaspoons (30mL) has killed adults - much less for children.
The other ~5% of the ingredients are the anti-corrosion chemicals (IAT, HOAT and OAT) which do wear out and it is in these chemicals only that most coolants differ.
Hope this was interesting & helpful,
Rumple
I guess my first question is what is the difference in colors? Changing my colors will it cause damage to the cooling system? Engine? What is it they are refusing to tell me?
Mary