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Connector Type can be drawn in exactly one Diagram Type
Diagram Type can draw zero, one or many Connector Type
These are the types of Connectors that can be drawn on a given Diagram Type. On an xUML state machine diagram you can draw initial, final and normal transitions, for example, whereas on an xUML class diagram you can draw generalizations, binary associations and association class relationships. More to the point, you cannot draw a state transition on a class diagram. So this relationship constrains what can be drawn on a given Diagram Type. (Though nothing prevents you from defining a new Diagram Type where this would be possible!)
Most Diagram Types will have at least one kind of Connector Type, otherwise the associated diagrams will just be a layout of unconnected Nodes. That said, there is no reason to require connections on any given Diagram Type.
A Connector Type is defined exclusively to a Diagram Type. Thus, transition on a state machine diagram may be defined differently than transition on some other kind of diagram.