Theatre of the Absurd refers to plays written largely in Europe in the late 1950s and influenced by Existentialism. Thus, existentialist philosophy is more of a broad umbrella term for a school of thought exploring questions of individuality and existence, while Theatre of the Absurd is a specific genre of drama. Existentialist philosophy is difficult to define, with Existentialist thinkers rarely coming to an agreement on its tenets. In general, though, Existentialism proceeds on the key concepts that existence precedes essence (a focus on authentic existence) and that absurdity or meaninglessness is part of existence.
The term “Theatre of the Absurd” was coined by critic Martin Esslin in 1960, using the term “Absurd” in the way Albert Camus used it in “The Myth of Sisyphus,” a 1942 essay. The “Absurd” refers to man’s struggle for meaning in a meaningless world. Probably the most famous play in this genre is Samuel Beckett’s 1952 Waiting for Godot. The focus of this play is man’s inability to overcome the absurdity of life and that everything is ultimately pointless.
Another distinction between existentialist philosophy and Theatre of the Absurd is that a fictional work may deal with existential concepts without the author necessarily seeing himself or herself as a proponent of the philosophy.
Existentialism, as a philosophy, allows for free-range thinking under the prospect that life may or may not have any purpose for living. This philosophy questions whether the constructs that we have built are worth following, and whether the ideas and philosophies that we follow are a realistic need to survive.
The theater of the absurd takes these notions to an extreme because of the need to illustrate "the point". Theater, as an art form, also tends to combine other elements such as realism and fantasy to fulfill the duties of entertaining an paying audience. This is an unfortunate reality, but it is reality nevertheless.
Therefore, existentialism will always allow for a number of diverse sub-constructs to surface as part of its philosophical tendency. The theater of the absurd is meant to show a few tenets of existentialism for the purpose of illustrating the point.
There are certainly differences. The most important difference would seem to be that Absurdist Theatre is a formally defined concept and existentialism is a rather wide-ranging body of thought commonly defined as a philosophy.
Absurdist Theatre can explore and express existentialist ideas, but existentialism certainly cannot be defined as a formal, abstract mode of theatrical presentation, theatrical writing, and self-referential drama.
(Existentialism is not necessarily characterized by self-reference as Absurdist Theatre often is.)