For the sake of this discussion, a stereotype is defined as something is generally confining a person/population/entity into a narrow box of fixed traits, while an archetype is a foundational short hand for a combination of traits that can be expanded or built upon, mixed and matched, etc.

There are a number of different categories for role-playing game related archetypes and stereotypes, and of course there are the famous archetypes discussed by Carl Jung, Joseph Campbell, Otto Rank, Lord Raglan, and many others. For this discussion we'll focus mostly on the following categories:

Gaming Player Stereotypes and Archetypes
Gaming Game Master Stereotypes and Archetypes
Role-Playing Game Player Character (PC) Stereotypes and Archetypes

The RPG Research and RPG Therapeutics Player Archetype Specialist roles:

See the Player Archetype Specialist Handbook by W.A. Hawkes-Robinson and Valerie Krepel for much more in-depth information.

Definitions

Since many of the terms used have multiple meanings depending on context, profession, training, background, culture, and even English language variants between US and U.K. English, the following definitions are provided for the terms used throughout this document.

Actions

the accomplishment of a thing usually over a period of time, in stages, or with the possibility of repetition.

Archetype

the original pattern or model of which all things of the same type are representations or copies.

Merriam-webster: https://www.merriam-webster.com/dictionary/archetype

Behavior

b : anything that an organism does involving action and response to stimulation

c : the response of an individual, group, or species to its environment

Cliché

1. : a trite phrase or expression; also : the idea expressed by it

2 : a hackneyed theme, characterization, or situation

3. Something that has become overly familiar or commonplace.

https://www.merriam-webster.com/dictionary/clich%C3%A9

Personality

a : the complex of characteristics that distinguishes an individual or a nation or group; especially : the totality of an individual's behavioral and emotional characteristics

b : a set of distinctive traits and characteristics

Stereotype

a : to repeat without variation : make hackneyed

b : to develop a mental stereotype about

Trait

a : a distinguishing quality

Trope

b : a common or overused theme or device

https://www.merriam-webster.com/dictionary/trope