Long ago, when wise men believed that buff, shirtless gods in chariots drove a ball of fire across the sky to provide light to us lowly humans, they named the light-giving fire ball “the Sun” (or the linguistic equivalent in whatever language those wise men spoke). The latin word for “the Sun” was “Sol,” whereby we now have the word “solar” to describe anything that has anything to do with the Sun – solar wind, solar rays, solar panels, etc…
For many hundreds of years thereafter, humans believed that the Sun was a unique celestial object. It was the only “sun”, so it was actually “the Sun.” The Sun, along with Earth, and the other planets that could be observed with the naked eye, would become known as the solar system. Again, until quite recently, it was believed that the Sun was the only sun, and thus the solar system was the only solar system and was therefore more properly called “the Solar System.”
A couple hundred years ago, even wiser men figured out that all of those bright dots in the sky that they called “stars” were actually other suns. Conversely, our Sun was actually just another one of those bright dots in the sky called stars. But we already had names for these other suns – or stars. Like Rigel and Sirius, Aldebaran and Altair, Vega and Regulus, and the list goes on and on.
Even more recently, scientists confirmed that many of the other stars – or suns – also had planetary systems, at least vaguely similar to our own. Not surprisingly, these other planetary systems are usually identified with their own host sun – star. So we would say the Gliese-581 System for the confirmed multi-planetary system orbiting the star Gliese-581, or the Kepler-20 System for the star Kepler-20′s planetary system.
Therefore, it stands to reason, that although people often use the term “solar system” (lowercase) generically when referring to the planetary systems of other stars, it is more accurate to reserve “the Solar System” (uppercase) to describe only our own “solar system” (lowercase), as it is the “solar system” (lowercase) that orbits the star “Sun” (or “Sol”).
But I’m no scientist.