How is chemical and dynamic equilibrium related?

I have been told that dynamic equilibrium is attained when the reactants and products of a system has achieved the same concentration or when their rates of formation are the same. And I also know that even though nothing seems to go on in a dynamic equilibrium there's still so much activity.
Now assuming I've got that right. I want to know how is chemical equilibrium any different from what I mentioned abt dynamic equilibrium.
Also can chemical and dynamic equilibrium coexist??




Background: It is generally the case that there is an energy barrier between reactants and products, sometimes called an activation energy, and this is smaller for reactants than products so that a reaction proceeds towards products. 


Suppose now that there is a reaction such that $\ce{ A \to B}$ and initially only A is present so that the rate of forward reaction is large, i.e. lots of A and almost no B make the forwards reaction faster than the reverse reaction. As soon as some B is present it can react back to make A, but $\ce{ B \to A}$ will be slow compared to $\ce{ A \to B}$ because there is less B (smaller concentration) and the activation barrier is larger so the 'rate constant' is smaller. 


Eventually the amount of A is reduced and B increased until both *rates* are the same and equilibrium is achieved. Note that the concentrations need not be the same, in fact they usually are not. Also note that molecules of A continuously convert to B; $\ce{ A \to B}$ and similarly B convert to A; $\ce{ B \to A}$ which is to say that the *normal* state of affairs is the 'dynamic equilibrium' and simply using the word 'equilibrium' implicitly assumes that this is the case. 


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