What is the difference between a (dynamic) Bayes network and a HMM?
From a similar Cross Validation question follows @jerad answer:

HMMs are not equivalent to DBNs, rather they are a special case of DBNs in which the entire state of the world is represented by a single hidden state variable. Other models within the DBN framework generalize the basic HMM, allowing for more hidden state variables (see the second paper above for the many varieties).
Finally, no, DBNs are not always discrete. For example, linear Gaussian state models (Kalman Filters) can be conceived of as continuous valued HMMs, often used to track objects in space.
I'd recommend looking through these two excellent review papers:

An Introduction to Hidden Markov Models and Bayesian Networks by Zoubin Gharamani
Dynamic Bayesian Networks by Kevin Murphy