It seems that you are conflating the terms model and diagram.
A diagram is just a visualization of a model or its part, it is not the model itself.
So what you can have is a single UML model representing your entire system and then you use different diagrams to see only parts of the model… in class diagrams you are focusing primarily on the structure of the model, in state machine diagrams you are looking at some particular behavior, etc.
But the metamodel describing the model is still the same, as described in the specification.
Some more tips/references that may help you:
- Read Annex A
- Class diagrams are focused on structural representation, so chapter 11. Structured Classifiers may get you started
- A chapter (such as 9.6. Operations) typically contains "Notation" and "Examples" sections that explain how the element is to be visualized in a diagram
- Diagram Interchange (Annex B of UML Specs linked above) and Diagram Definition describe the meta-model behind diagrams, however this may be yet something else then what you are looking for