The two terms are interrelated, but definitely mean different things. Think of a literary theory as a lens through which we look at literature. There are many different schools of thought when it comes to literary theory, and each theory focuses on different aspects of a text. For example, Feminist Theory is concerned with the power relationships and sense of stereotypically male vs. female identity present between male and female characters. Reader-response theory, on the other hand, is mainly concerned with the emotional effect of a text on individual readers and correlations with readers' personal experiences. There are many of these theories. Some of the other major ones are: Formalism, Psychoanalytic, Marxist, Structuralism, Post-Colonial, Deconstruction, and Queer Theory. (See reference links for more specific information.)
Once you know what theory you're working with, you're ready to read (or write) some literary criticism. Literary criticism is the "study, evaluation, and interpretation of literature" (enotes). This is where the correlation with theory comes in--literature is far too broad and subjective to just evaluate and interpret on a generic basis. Thus, a critic usually has a specific lens to look through. (A theory!)
CASE STUDY: So, let's say that I wrote a piece of literary criticism on the original version of the fairy tale "The Little Mermaid," in which a mermaid falls in love with a prince who she can't have. She is offered a chance to kill the prince so he cannot marry a human princess, but she cannot do it and instead dies of a broken heart. She then becomes a fairy of the air and gets a chance to watch over sailors and gain a soul which she would not get as a mermaid. Nifty tale, right?
Ok, so if I were to right a piece of literary criticism that was informed by Reader-Response theory, I would talk about the nostalgia invoked by the tale, and how it relates to the universal experience of unrequited love, perhaps how we all feel that a part of us "dies" with each failed relationship. However, if I were to write a piece of literary criticism based on Feminist theory, I would spend the bulk of my time asserting how this story reinforces the role of women as submissive, self-sacrificing, passive beings and how it is ill-fit as a bedtime story for young women who we want to grow up to be strong leaders.
The two terms go hand in hand. P.s. Also, be aware that sometimes literary theories are referred to as "schools of criticism," thus making the two terms interchangeable in that scenario. Hopefully, this answer clarifies the subtle difference.