Is there any flavor difference in heated sugar (e.g. cotton candy)?

What Rincewind42 says about caramelization is true in itself, but it doesn't apply here. Cotton candy is made from sugar syrup at the hard ball stage (130°C), so too cold for caramelization. Caramelization only starts occuring at 160°C and above. In fact, caramel has a very different texture from sugar, so it is practically impossible to spin cotton out of it. It makes spidery, unendly elastic strands, unlike the brittle cotton candy strands. Plus, it is visibly brown, and tastes very different from sugar, so you'd notice it when eating the cotton candy.

The flavor of cotton candy is indeed sugar (unless it has had something else added). But taste is not the same thing as flavor. Things taste different to us based on texture, aroma, color and food name. (I once read about a study made with unusually colored puddings. People who had eaten cherry pudding with yellow coloring were sure they are eating banana or lemon, and they were convinced the pink vanilla pudding was strawberry). So it is entirely possible that a gelato customer who eats a gelato called "cotton candy", has lots of sugar and is painted a pastel color will perceive it as having a different taste from non-flavored ice cream which has lots of sugar, but not the color or the name, especially if the texture of the "cotton candy" flavor is tweaked a bit.

Cotton candy sugar comes in several flavors:

Cotton Candy Express sells grape, cherry, pink vanilla and raspberry.

Flossugar comes in a bunch of flavors like vanilla, banana, and blue raspberry (the actual names of the flavors are pretty weird).

Based on that, I'd guess that the "cotton candy flavor" is whatever flavoring they usually put in pink cotton candy, which seems to be just vanilla.

As @Brendan said there is flavor added to cotton candy. The mixtures aren't just sugar. The flavoring comes from an ingredient called flossine. If my memory serves correctly it is manufactured by Gold Medal, and is basically some proprietary mixture of coloring and flavor.

I believe the standard flavor is cherry. The last time I ran a cotton candy machine was a couple years ago for a church fall festival.

You can just run a plain sugar through the cotton candy machine, but it wont give you the taste you are looking for.

To answer your question, there is a chemical change in the sucrose as it moves from crystal to liquid form, but nothing that I believe would affect what we can taste. It is all really in the flossine.

FYI, if you are looking for that flavor in something else, like a cake or ice cream you can buy the flossine concentrate, and use it for whatever. Just make sure you aren't using any other flavors that will destroy the flavor profile of the flossine.

Hope this helps with what you are looking for.

When the sugar is heated to make the cotton candy, it will caramelise. This causes many chemical changes. The following clipped from wikipedia:

Caramelization is the removal of water from a sugar, proceeding to isomerization and polymerization of the sugars into various high-weight compounds. Compounds such as difructose anhydride may be created from the monosaccharides after water loss. Fragmentation reactions result in low-molecular-weight compounds that may be volatile and may contribute to flavor. Polymerization reactions lead to larger-molecular-weight compounds that contribute to the dark-brown color.