Phantoms

Phantoms are a type of undead. In common understanding, phantoms are either synonymous with ghosts or a specific kind of ghost. In Monster High, they are still undead and elusive, but solid.

Etymology
"Phantom" comes from the Ancient Greek word φάντασμα (phántasma), which can be translated as apparition, vision, and fantasy. Phantom From Middle English fantom, fantum, from Old French fantosme, from Latin phantasma, from Ancient Greek (phántasma).

c.1300, fantum "illusion, unreality," from Old French fantosme (12c.), from Vulgar Latin *fantauma, from Latin phantasma "an apparition" (see phantasm). The ph- was restored in English late 16c. (see ph). Meaning "specter, spirit, ghost" is attested from late 14c.; that of "something having the form, but not the substance, of a real thing" is from 1707. As an adjective from early 15c.

Phantoms in Monster High
The Monster High phantoms are Operetta and her parents as well as Dr. Boolittle. Mr. Rotter is not confirmed to be a phantom, but since his design is based on Lon Chaney's Phantom of the Opera, he is logically one too. Based on these five, phantoms can have purple skin, green skin, and blue skin. Invisi Billy notes in his New Scaremester diary that he is regularly mistaken for a phantom, suggesting they can have white skin too.

Operetta was one of the four characters originally designed for Monster High, but during the three-year development period her role was given to the mummy Cleo de Nile. Operetta was given fictional presence in Holt's Basic diary, but didn't make a personal appearance until late in Volume 2 of the cartoon and wasn't fully incorporated until the Campus Stroll line. She and Howleen Wolf, if perhaps in name only, had to wait the longest of the original four to be included. In Operetta's case, this presumably was done because the Phantom of the Opera is not necessarily a monster in the source material and Operetta would fit better as a building stone of the franchise than a foundation pillar.

Prior to Operetta, the cartoon introduced Mr. Rotter. He is notably not one of the original teachers as introduced in the Fearbook, yet has grown to be one of the three most prominent members of the Monster High staff in fiction. As aforementioned, he is designed after the Phantom of the Opera as the character appeared in the 1925 movie The Phantom of the Opera. In Ghouls Rule, he even displayed a preference for using secret passageways like the Phantom of the Opera is known for. He is not the Phantom himself though, who is a separate character but coincidentally also a (night) teacher at Monster High.

Because phantoms in Monster High do not match the ghost-like qualities of the source creatures, they are among the most ill-defined species in the franchise. Both Operetta and Rotter prefer to control their own coming and going, but voice powers seem to be exclusive to Operetta and potentially her family. Little is known about Dr. Boolittle but for the fact he has no problem spending decades away from society for the purpose of research. As such, reclusiveness appears a defining characteristic, which would be based on the behavior of the Phantom of the Opera in The Phantom of the Opera.