When the context is science, the word "theory" means a logical/mathematical framework which tries to explain the phenomena. Infact in science "Theories" carry some "Claims" or "Predictions" while every sub-discipline of science could be presented in many number of theories. But in "Mathematics" the word "Theory" seems to merely refer to a sub-discipline of a mathematical field of study. For example I could call "Number theory" the discipline of "Studying Diophantine equations" or "Group theory" the "Study of certain types of algebraic structures(namely Groups)" or "Differential equation theory" the "The methods of solving differential equations".
Does the word "Theory" in mathematics have some special meaning like bringing some claims or predictions or is it just a reference to the mathematical sub-discipline we are studying?