Every story is different, and oh, is that an understatement! Just look at the dragons in them.
In the Deltora books by Emily Rodda, the colors of dragon scales depend on which clan they come from (clans are divided by regions). In The Dragonriders of Pern books, colors indicate gender and rank. Golds and greens are female, with golds being superior to all other colors. Bronzes tend to rule the roost as far as males go, still subordinate to gold but tending to mate with gold. Browns come next and then blues (also both male). Size is even indicated as the dominant colors are also the largest – Gold being the largest dragon and down to green and blue (the smallest ones).
In other books, Dragon Slippers by Jessica Day George uses colors as a way of identifying the dragons. It’s a bit like how people used to use their parents’ names (John’s son became Johnson and so forth). Instead, you have characters like Shardas the Gold and Velika Azure-Wing.
On the flip side, there’s Dealing with Dragons where color doesn’t matter. The dragons are all manner of colors, which means nothing. However, the number of horns indicates male, female, or youth (young dragons haven’t picked a gender yet).
These are the main examples that come to mind, and there are plenty where attributes are nothing but an accident of genes as is, perhaps, more realistic. If I missed any, though, feel free to leave them in the comments!