A rigid body can be either active or passive, and an active rigid body can be dynamic or not:
The documentation says about the passive type the following:
Object is directly controlled by animation system. Thus, this type is not available for Rigid Body Dynamics.
And about dynamic:
Enables/disables rigid body simulation for object.
I see no difference between the two. As far as I can see, both of these mean that the object is not moving, but still participates in collisions.
Note that I know that there is already a similar (unanswered) question...: rigid bodies: passive vs not-dynamic
... but I decided to ask again, because I could not reproduce the scenario in that question (extruded planes behave for me the same as non-extruded).
EDIT As f59838 answered, there is a tutorial, where Andrew "Blender Guru" Price says that "We want our chain to swing, so we need the top link of the chain to be stationary. Select it then go to the Physics panel and uncheck Dynamic. This is different to Passive, because it’s still using it’s Mesh collision data but it won’t move."
I think this explanation is not correct, because passive objects also can have a Mesh setting for the collision shape. It is true that in this special case (toruses) it does not work - after a few strange movements, they fall - but this seems like a calculation error. In fact, if you double the Steps Per Sec in the Scene/Rigid Body World, the toruses won't fall (although the movements are still strange)
So yes, there is some difference, but it is not what Andrew said.