Hidden Markov

Hidden Markov is termed as statistical markov model in which the system follows markov process with hidden states, where the term "statistical" refers to how one or more random variables are related to one or more variables.

How hidden markov different from Markov chains?

The Markov chain consists of set of finite states, whereas the hidden markov consists of set of hidden states.
The Hidden markov can be represented as the dynamic Bayesian network. (i.e.) Hidden Markov can also be said as the Combo of Markov chain + dynamic Bayesian network.