I apologize if this question seems overly basic. I was wondering how to recognize what a theory is really saying, as opposed to the explanation/corollaries that are drawn from it.
As an example, take Einstein's theory of special relativity. Would the theory be that inertial reference frames are indistinguishable and the speed of light is constant? Would the theory be that the coordinates of an event can be transformed from one system to another using the Lorentz transformation? Would the theory be a statement of time dilation and length contraction? I apologize if this question is vague. I am just wondering if there is any way to say that "this is the theory" and from "this", I can derive everything else.
Another, rather basic question, I have is on the relationship between theories and models. To my understanding, models are tools used to understand/visualize theories. I was wondering how physicists go about creating such accurate models. For instance, the atomic model of the universe is extremely powerful and is consistent with all of the physical theories I can think of. In fact, it seems that this model of the universe can be used to predict phenomena that are not immediately obvious from the theoretical equations. I was wondering how it is possible for us to create such accurate models. Have there been instances where we have come up with invalid models for valid theories? Have there been instances where we have come up with valid models whose underlying theories were found to be invalid?