In terms of Latin, sol is just as generic as stella is. (Modulo the fact that there is only one sun.)
If you want to object that "Sol" is the name of an individual star, and that "solar radiation" is named after that name, in spite of the capitalization, rather than deriving from the Latin word, then you can't really make your arguments based on what the words mean in Latin.
> In terms of Latin, sol is just as generic as stella is. (With the caveat that there is only one sun.)
We can argue over whether the idea of a generic label for a class that by definition has exactly one member is coherent, but I don't think that's necessary: stars that aren't the sun are stella and aren't sol, whether you take the latter to mean “Aren't the single particular entity named ‘Sol'” or “Aren’t one of the members (of which there are exactly one) of the class whose members are designated ‘sol’”.
There's a reason they are “extra-solar planets” and not “other-solar planets”.
It was a class with one member at the time Latin was spoken. It's the same class now, but with many members.
Once you admit that the sun is an example of a star, "sun" becomes a deictic reference.
Note that "Sol" is not the English name of our sun. We call it "the Sun", at the same time that we're happy to say that planets in other stellar systems have suns of their own. "Sol" is a name internal to academic astronomy, much like the name "bufo bufo" for what are actually called "toads".
