I'll take a stab at this, but I would be interested in other people's points of view as well. The 1935 EPR paper's abstract says:
In a complete theory there is an element corresponding to each element of reality. A sufficient condition for the reality of a physical quantity is the possibility of predicting it with certainty, without disturbing the system. In quantum mechanics in the case of two physical quantities described by non-commuting operators, the knowledge of one precludes the knowledge of the other. Then either (1) the description of reality given by the wave function in quantum mechanics is not complete or (2) these two quantities cannot have simultaneous reality. Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that if (1) is false then (2) is also false. One is thus led to conclude that the description of reality as given by a wave function is not complete.
Note that they don't even claim to be able to give a definition of "reality," only a sufficient condition for reality. The basic point of view being described is one that Einstein frequently expressed by saying that he liked to think that the moon was still there even when he wasn't looking at it.
Later in the paper, they say:
The elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements.
Note again how their caution leads them not to claim to be able to give a definition. My understanding of what is being expressed here can be given by the following analogy. If you believed in Aristotelian physics, then you might say that we could decide whether a particular object is "really" moving or not. But then later experiments would invalidate Aristotelianism, and we would end up concluding that you can't say whether an object is "really" moving. EPR seem to be anticipating a future, better theory that would replace quantum mechanics, and they don't pretend to know what would be the correct "elements of reality" in such a theory. (My analogy is inexact, because in my example, motion lacks reality because it's frame-dependent, whereas in EPR's example, a lack of reality comes from the fragility of microscopic states.)
EPR were modest and anticipated that later work would clarify the correct definition of reality. People certainly have continued working on how to define it, but I don't think there has been any conclusive result. Part of what makes me think this is the way that realism has been treated in some recent work by Pusey and collaborators. Although I'm still in the process of trying to digest this stuff, Pusey seems to feel the need for a very different framework for discussing realism than anything that was in use in the era of J.S. Bell. In the PBR paper, Pusey et al. split points of view on quantum mechanics into several categories (quoting):
Wavefunctions are epistemic and there is some underlying ontic state. Quantum mechanics is the statistical theory of these ontic states in analogy with Liouville mechanics.
Wavefunctions are epistemic, but there is no deeper underlying reality.
Wavefunctions are ontic (there may also be additional ontic degrees of freedom, which is an important distinction but not relevant to the present discussion).
Here, "ontic" basically means it's real, while "epistemic" means it's only a description of our knowledge. In this lecture, Pusey refers disparagingly to "the kind of naive realism that you find in textbooks." The implication seems to be that the notion of realism was not on a firm footing in the past -- and I'm not sure that he even means to imply that it's on a firm footing now, either.
So the impression I get is that "realism" is a word that's still in search of a definition, and that may have outlived its usefulness. What seems to have happened historically is that people came up with results like the Bell inequalities, which shocked their intuition. They tried to come up with a label to explain why they were shocked, and the best label they could come up with for the sensibility that was offended was "realism."
could you help me to distinguish the difference between Scientific Realism, Realistic, and Realism?(Or are they the same?)
As far as I know, scientific realism means the same thing as realism. I have not come across "realistic" used as a synonym.
Does either one of them imply the deterministic?
No, I don't think so. E.g., the stock market is nondeterministic, but that doesn't seem to raise any issues with realism of the type described by EPR.