What are the differences between Oracle Turing Machine and PAC? I am having difficulty understanding the difference between PAC and Oracle Machines.  I cannot compare these two in terms of uncertainty and physical effort.
The degree of uncertainty we can tolerate in a system has been discussed ever since Turing. His oracle machines
answer questions with maximal uncertainty, and zero physical work, because they are oracles. They don't have to justify their answers.
His automatic machines, or a-machines, are what we now call standard TM. In the probabilistic
version, there is no new class of functions that we can compute which we cannot compute with deterministic TM.
The Probabilistic TM can decide which route to take depending on probabilities assigned to its transitions. In the simplest case of binary branching at every state and total random choice, it flips a coin about which route to take.
We know that in doing so we don't get anymore computable function than what we get with nondeterministic TM, but we might get to some answers more quickly.
PAC idea, however, changes things. 1-epsilon is the amount of uncertainty a PAC problem solver can tolerate in calling a solution 'approximately' correct. If epsilon=0, then you get maximal tolerance.
How this idea can be related to Turing's oracle, and to relation between certainty and amount of physical effort.
An oracle access to a random oracle can simulate the effect probabilistic TM's have. However, oracle machines aren't limited to using a random oracle, you can specify whatever oracle you would like, to any problem - no matter how hard the problem is, and a TM with an oracle access to it would solve it in constant time.
So, in this line of thinking - an oracle machine can be thought of as a really general extension of the probabilistic case.
I don't know if this answered your question, but I hope I managed to help a little!