Literary criticism and literary theory are terms that have, in the last century, become interchangeable. Now, to say either is to refer to the study, critique, analysis, and interpretation of literature.
Prior to the advancement of literary theory, literary criticism was mainly concerned with critiquing what is good and what is bad literature, what literature is (how it differs from other kinds of writing), and chronicling the history of literature.
Many Western critics say that literary criticism significantly began with Aristotle, who examined the author's intent and plot structure (most notably with Oedipus Rex). Thus began the evaluation of what literature is (according to structure) and what makes it good or bad. Moving up to the 18th century, the Romantics wrote poetry but they also wrote poetic theory, evaluating what poetry had been (historically) and what it could be in the future. Literary theory really exploded in the 20th century, becoming more diverse, specialized, and complex. With the advent of theory, literary criticism was still practiced as an historical, critical analysis of literature, but it also began to acknowledge things other than the author and text.
Some early 20th century Formalist and New Critics (i.e. Cleanth Brooks) believed that a literary text was an autonomous object. So, to study its "literariness," one would focus on the form and meanings within the text itself: examining tropes, plot construction, metaphors, images, organization, etc. However, theorists concerned with cultura and politics emerged and created other branches of theory such as Feminism, Marxism, and New Historicism. These theorists believed that a reader, critic, or theorist could not focus just on the text. The critic had to evaluate literature in terms of its historical context, authorial background, and the sociological connections in the text.
For example, when evaluating a text such as Things Fall Apart, it would make sense to look at colonial and post-colonial theories as well as the structural formulation of the text itself. In fact, it seems silly to ignore the historical and sociological aspects of a literary text that is about precisely those issues. As a result of this realization, most theorists/critics embraced other theories, in addition to Formalism and New Criticism, to address the issues that a merely textual analysis would not address.
From Aristotle to the present, literary criticism has branched out significantly, becoming a multi-disciplinary field. Literature is a product of history; literature can also influence history. To incorporate this reciprocal relationship, theory had to expand its scope to address the historical and social issues at play in that relationship.
Acknowledging history (real life: sociology, psychology, politics, etc.), literary criticism also began to address the impact of the reader. In "The Death of the Author," Roland Barthes proposed a shift of focus from the author to the reader because once a text is in the hands of the reader, freedom of interpretation opens up and can become more diverse. Focusing only on the text or authorial intent limits theory's uses:
To give an Author to a text is to impose upon that text a stop clause, to furnish it to a final signification, to close the writing.