Markov chains are basically finite state machines with statistically weighted edges (arrows). Is a Markov Chain the Same as a Finite State Machine?

Three lifetimes ago I was using Monte Carlo simulations for optimizing queuing in manufacturing processes.

The mention of Claude Shannon reminded me that I have a book on my shelf I still haven’t read: The Information: A History, a Theory, a Flood

I wonder if this paper is as interesting as it sounds: Problem Solving is Often a Matter of Cooking Up an Appropriate Markov Chain (PDF)