There are four different types of classes in the game: Base, Specialist, Racial Paragon, and Prestige.
Base Classes
A “Base Class” is any class with a full 20 level progression that has no or very few prerequisites for entry. Game Masters are encouraged to allow players to choose freely from these classes, but each GM must make a personal decision about what is and isn’t allowed in a campaign, and the relative prevalence of such character classes in the campaign’s world. Each new class presents interesting new character themes and special abilities.
NPC Classes
An NPC class functions exactly like a base class, except that they are only appropriate for non-player characters or for extremely low power games where the normal classes aren’t used. While nothing prevents a player character from taking levels in an NPC class, the benefits are so minimal as to not be worthwhile when compared to any other class option.
Specialist Classes
A specialist class takes one or two narrow aspects or a specific concept of a character and heavily focuses on expanding or improving only those aspects to the exclusion of other abilities. This is typically one specific class feature, feat, or other relatively narrow option. Specialist classes, by design, miss out on some of the features available to a base class to focus on strengthening their focused concept beyond what is typically available.
Specialist classes have very specific but typically easy to meet prerequisites for entry, usually in the form of having access to the class feature or other ability that the class focuses on improving. A specialist class’s prerequisites are usually met almost automatically by taking levels in a related base class.
Specialist classes are not typically available before 4th level, requiring a character to have at least 3 other class levels before taking a specialist class. The classes are also typically only 3 levels long, though some may extend to 4 or rarely 5 levels.
Racial Paragon Classes
Similar in some ways to a specialist class, a racial paragon class focuses on expanding the innate racial abilities of a specific race. Like a base class, racial paragon classes may be taken at 1st level; however, only members of a given race (or of a related subrace) may take levels in a racial paragon class.
A character can never have levels in more than one racial paragon class, even if they are permanently changed into a new race, unless a specific class feature of allows the character to take more than one paragon class, such as with the Half-Elf Paragon.
Prestige Classes
Prestige classes allow characters to gain new, unique, and exceptional abilities beyond those available to base classes. Similar to specialist classes, a prestige class has specific requirements that must be met before a character can take levels in the prestige class. These tend to be fairly strict, and most characters will need to plan in advance to be able to meet the requirements. A character cannot take any levels of a prestige class until the character has already fully met the requirements.
While a prestige class might grant new uses of existing abilities or advance existing class features, most tend to grant new abilities and focus on those new abilities. For example, the Purifier of Minrhet prestige class progresses a character’s channel divinity ability, but it primarily grants new abilities to smite and produce other supernatural effects. The Mystic Theurge progresses both arcane and divine spellcasting, but its primary focus is on granting new abilities to modify how spellcasting works. On the other hand, the Black Abbot class grants all new abilities but does not progress or improve any existing class features and, in fact, actually hampers the use of certain class features you might already possess.