Difference between a turing machine and a finite state machine? I am doing a presentation about Turing machines and I wanted to give some background on FSM's before introducing Turing Machines. Problem is, I really don't know what is VERY different from one another.

Here's what I know it's different:


  FSM has sequential states depending on the corresponding condition met while Turing machines operate on infinite "Tape" with a head which
  reads and writes.
  
  There's more room for error in FSM's since we can easily fall on a non-ending state, while it's not so much for Turing machines since we
  can go back and change things.


But other than that, I don't know a whole lot more differences which make Turing machines better than FSM's.

Can you please help me?
The major distinction between how DFAs (Deterministic Finite Automaton) and TMs work is in terms of how they use memory. 

Intuitively, DFAs have no "scratch" memory at all; the configuration of a DFA is entirely accounted for by the state in which it currently finds itself, and its current progress in reading the input.

Intuitively, TMs have a "scratch" memory in the form of tape; the configuration of a TM consists both of its current state and the current contents of the tape, which the TM may change as it executes.

A DFA may be thought of as a TM that neither changes any tape symbols nor moves the head to the left. These restrictions make it impossible to recognize certain languages which can be accepted by TMs.

Note that I use the term "DFA" rather than "FSM", since, technically, I'd consider a TM to be a finite-state machine, since TMs by definition have a finite number of states. The difference between DFAs and TMs is in the number of configurations, which is the same as the number of states for a DFA, but is infinitely great for a TM.