Juan, Bal'Shamir is a red star system (Class M) about 12.5 light years from the sun (Sol) at about 258 degrees in the Spinward quadrant. The colors of the names tell you the system class and how many mineral worlds the system has. All red (Class M) systems have three mineral worlds. The graphic on the left clearly shows the colors of each system class and the number of mineral worlds associated with them. Since some multi-star systems (binaries and tertiary systems) have more than one class of star, it is important that the system names provide color-coding to clarify the number of mineral worlds at the multi-star system.
I don't even see the "D3 & 4" to which you refer.
I don't know how much you may be into astronomy, so forgive me if I seem patronizing. Our sun is a class G2 yellow star. Class K & M stars are smaller than our sun while class F & A stars are bigger. (There are no class O & B stars in our close neighborhood, but these are bigger yet. Rigel in Orions left knee is a massive class O star I believe.) Although we can't know for certain, it is reasonable that the mass of the system primary (the star or stars) is an indicator of the number of planets and moons that may be orbiting around the primary. The planets and moons are the source of materials and resources needed to build and power starships (as well as other industries supporting the economy of the system's owner. But only a few star systems have the sophisticated technologies and work force to actually build starships. These are the eight homeworlds with shipyard facilities in the game. They have the purple circles around their star symbols. To increase the productivity of your shipyard to its maximum, you must acquire additional systems (stars and their worlds) to provide extra resources. It takes 45 mineral worlds to bring a shipyard to its maximum production of 15 starships each turn (year).