It's my understanding that the Sun (uppercase) is used to refer to our sun/star, because it is The Sun. Latin name is Sol, hence the Solar System. Even the tag (lowercase sun) on this post has the caption "Questions regarding the closest star to Earth, at the centre of the Solar System."
Other planetary systems have their own stars, which I understand are called a sun, in the context of that planetary system.
I've tried my best to find a credible source that exoplanets indeed have their own suns, and that the term "sun" doesn't just refer to our Sun. I have only found this one website that backs this up: http://curious.astro.cornell.edu/physics/78-the-universe/stars-and-star-clusters/general-questions/346-what-is-the-difference-between-a-star-and-a-sun-beginner
It seems to be common knowledge in the scientific community that this is correct, but I can't find anything else online to back this up. Help?