“Quantum theory” is the original name for the field that became known as “quantum mechanics” (which see). The connotations of the two terms are somewhat different.
Using the term “quantum mechanics” emphasizes the mathematical equations of this field. From 1900 to the mid-1920’s, prior to the development of key equations, this field was called “quantum theory.” In the 1920’s and 1930’s, when key equations were developed, the field became known as “quantum mechanics.” This is on analogy with the equations of classical mechanics developed by Isaac Newton. The term “quantum theory” is usually applied only to the early period, prior to the development of the key mathematical equations of the field.