Difference between State Space and Sample Space Aren't they both the same?
According to me they are just different terminologies used for different types of systems. What I understand is that sample space is used when we talk about static systems and state space when we talk about dynamic systems. Am I correct? If not then what exactly is the difference between them?
My teacher had asked for the state space in Markov Chain questions, so I'm guessing that state space is used only in dynamic systems? She said that if we roll 2 dice then the sample space will be {1,2,...,6},
but the state space will be {(1,1),(1,2),...,(6,6)}.
But as far as I remember, the sample space for rolling 2 dice is
{(1,1),(1,2),...,(6,6)}.

"State space" is used in lots of areas of math. For instance, "all possible positions for a particle, along with all possible velocities at those points" might be a state space for analyzing particle motion, or "all the possible pairs generated by rolling two dice" might be a state space for a gambling question. (see edit below)
"Sample space" usually means that in addition to a set of states there is also a "probability function" associated with the state space, which gives you a way to say which states are more or less likely to occur. 
So samples spaces are examples of state spaces, but there are a lot more different types of states spaces than just sample spaces. However, if you're only taking Stats you can expect them to be used interchangeably. 

Edit: According to Wikipedia, my example of "all possible positions ..." should be called a "phase space", because it's continuous, and state space is only proper for discrete spaces, but I'm pretty sure I've heard "state space" used in both discrete and continuous instances.
