I think the wording means that you would receive both. It specifically says that the same race can be used for multiple challenges and that it is possible to receive two different medals at the same event. Scroll down to the bottom and read the eligibility section.
https://www.rundisney.com/coast-to-coast-race-challenge/
It actually gives an example that running Light Side at
Disneyland and Princess means you receive the C2C. It goes to say that if you also finish Tinker Bell, you would also receive the pink C2C. The one caveat is that runners can only receive one
unique C2C Challenge medal per year.
And a runDisney rep told me at Light Side that Kessel Run finishers would also receive the 10th anniversary C2C. I did not actually ask her. She saw me looking at the medals and told me that Kessel Run also eligible for C2C.
Now, as I understand their website and factor in what the sales rep told me:
1. You can use the same event (Dark Side/Kessel or Tinker Bell/Pink C2C) to also receive the original C2C in addition to the corresponding special medal (Kessel or Pink C2C). Note that the website C2C page specifically mentions that you can use the same event to receive two medals. Since Star Wars and Princess/Tink are the only ones that offer a specific themed C2C, this only applies to those two races.
2. My interpretation of the only earning one
unique medal means that if you finished a WDW Marathon weekend and Light Side or Light Side and Princess, you will not receive the C2C after finishing Dark Side because you already earned the original C2C, but will still receive the Kessel Run. Likewise, if you finish Light Side and Dark Side, you will not receive the C2C if you run Tink or Disneyland or Avengers because you already received the original C2C at Dark Side. You would however receive any other medal (weekend challenge events) you registered for.