You forgot "Conquest" (which covers generic villains like Tatanga and one-shot villains like Wart and Smithy), which is probably meant to be a Heresy of Bowser. There is only one Dark Star (in "Bowser's Inside Story", I do believe), but there is a Ztar (pronounced "zuh-TAR"). "Mario Party I" and "Mario Party IV" both mention Ztars as the antithesis to Power Stars. They possess negative energy and literally cancel the effect of any Power Star they come in contact with. (As such, one Ztar deletes on Power Star.)
Excluding the RL-style suns, there are three primary types of Star in Mario's world.
1. First are the Star Spirits and their baby equivalent, the Star Kids. Star Spirits are gods in the Mario World (and there are seven chief Star Spirits) and Star Kids grow up to become lesser Star Spirits in Star Haven. The Seven Star Spirits are near-omnipotent, but they can be sealed off and their powers limited to simple telepathy. Star Kids and lesser Star Spirits execute wishes not granted by the Star Rod, often by direct action. (Twink, for example, directly granted Peach's wish for aid by appearing to her.) Star Kids cannot attack (although they can intimidate) and possess no supernatural abilities.
2. Second are the Power Stars ("Super Mario LXIV"). Much like Star Spirits, they have an adult version and a baby version. Baby Power Stars are called Lumas ("Super Mario's Galaxy I"). They are considered the fundamental essence of life and form Galaxies (which house all life on their own) and RL-type stars (like the sun) to sustain life. Power Stars are used to seal and unseal any given portal or world ("Super Mario LXIV", "Mario Party" series). To create life, or galaxies of sun-like stars, a Power Star (or, in an emergency, a Luma) must destroy itself, as seen in the ending of "Super Mario's Galaxy I". (I am not sure if they die to unlock minor doors, though.) The overseer of all Power Stars is Rosalina, but she is depicted as a caretaker and not as their deity. Ergo, the Star Spirits apparently control Power Stars indirectly and Rosalina was one of their Chosen Ones to help them grow. When sufficient amounts of Power Stars congregate, they can merge and form Grand Stars. The First Grand Star was obtained at the very end of "Super Mario LXIV" after Mario destroyed Bowser. It took him out of the Bowser Dimension and returned him to the castle entrance, successfully unsealing Princess Peach. Grand Stars seem to have reality-warping powers and can unlock or seal anything, even living beings. They are also sources of boundless energy and are critical to the creation of all heat and light in the Mario universe.
3. Then, there are the Starmen. These might be Power Stars, or they might be their own thing. They grant their holder invincibility and inundate him with great power, speed, and control over themselves or their vehicles. If the wielder so chooses,
he can kill anyone with a Starman by touching them or do them harm, but he can also withhold that ability. Starmen are power-ups and live in relative harmony in the Mushroom World with others. Catching one activates its power and, like Power Stars, only by the destruction of a Starman can its powers be deployed. Starmen can be evil, such as the Angry Sun in "Super Mario Brothers III". (Though the Angry Sun could also be a lesser Star Spirit, given that he is corporal.)
