These are the known classifications:
Class 6 Gas Giant - "Extreme Risk"
Class 7 Gas Giant - "Broken Bow"
Class 9 Gas Giant (Q'tahl Class Gas Giant) - "Sleeping Dogs"
Class D Planet - Star Trek II: The Wrath of Khan
Class H Planet - "The Ensigns of Command"
Class J Planet - "Starship Down" (a type of gas giant)
Class K Planet - "I, Mudd"
Class K Planet (Transjovan) - "The Royale"
Class L Planet - "The Chase"
Class M Planet - "The Cage"
Class M Planet, Type IV - "The Bonding"
Class N Planet - "Night Terrors"
Class T Planet - "Good Shepherd" (a type of gas giant)
Class Y Planet - "Demons"
Type 4 asteroid - "Practical Joker"
Type C asteroid - "A Matter of Time"
And, there are types of asteroids from A to N. The type is based on size. ("Metamorphosis")
And, there are types of atmospheres from H to M. ("Metamorphosis")
I can't make sense of this.
In the Star Trek: Star Charts, planetary classifications are determined by many factors, including the diameter of the planet. Interestingly, there is a gap - between 15,000 and 50,000 diameters - for which there is no classification, and Neptune falls into this range.