The difference between Performance and Theatre begins with specificity. Performance is a broad term, including many different forms of entertainment and storytelling. Performance can mean anything from just simply the act of doing anything to a Commedia Dell'arte performance of The Servant of Two Masters in full Italian costume. Theatre is a category of performance. Dance, Concerts, Sports, these are all performances, but not Theatre.
In order to draw a distinction between these other forms of performance, I must clarify what these two terms mean.
Performance, a general concept of presentation can mean either
Performance is not a singular thing with a singular purpose. It is a category of many forms of action and/or entertainment.
Theatre is a kind of performance, a category, or a type. Aristotle in The Poetics lays out a formula for the art form of Theatre:
Of course, Theatre has become more complicated since Aristotle's time; often it includes some level of social impact, does not necessarily include music, uses various of levels of spectacle, and illuminates a range of depth and struggle in the human spirit. This is what makes Theatre different from other forms of performance. In Some Thoughts on Playwriting, Thornton Wilder distinguished Theatre from other art forms with four characteristics that are unique to it:
Aristotle's formula for the composition of a theatrical work paired with Wilder's distinction between this art form and others help clarify what is and is not theatre. For example, a Basketball game has elements of theatre, but it is not the same thing. It lacks a plot and thought/theme/ideas. It has a structure, but that isn't the same as plot and theme. The game is heavily concentrated on spectacle and rather than watching characters, spectators (not audience members) watch real people playing a real game vs. something imaginary. Another difference is in those who observe the two; an audience must hear the show in order to experience it. A basketball game must be watched, but does not necessarily need to be heard to be experienced. These key differences show that it is a performance, but it is not theatre.
It is important to delineate these types of performance to understand their format and function and to observe them analytically. To analyze types of performance, there must be clarity about what specifically each kind of performance is. Anyone who watches a play, movie, dance, concert, or sporting event enhances their experience and is able to both analyze and appreciate the type of performance to a higher degree. Anyone who wants to do that can only do so by understanding the distinctions as well as the similarities.