There is no one answer and semantics sometimes even negate the question. On the smaller systems and machines I design, the answer is 0 Ohms or something very close to that. And IMHO any two points that are termed Earth should be able to be tied to the same point, namely Earth, without any disturbance or hazard. This is not always true of the systems others design or their use of the terminology. I make a clear differentiation of Earth, Ground, Common and Neutral. Earth and ground should be the same, but the term "chassis ground" is common in electronics. And the terms Earth ground and Instrument ground and power ground, are also frequently used. This implies that there is a difference in grounds. Unfortunately the same seems to apply to Earth in locales where Earth is the term used where we (in the US) would use ground. So you see, without a lot of context, it is not possible to be sure even of what you are asking, much less provide a simple straightforward answer. If the answer is not 0 or a very small resistance, IMHO they should not be called the same thing, but that is just my opinion. Without schematics or carnal knowledge of the system, you probably can't know for sure, which is the problem. If you have schematics or access to the designer, you can. If two points are shown as connected together or routed to the same point or symbol (as in the case of recognized ground and chassis ground symbols) you can safely or at least arguably. presume that they should have low resistance. And yes, this is a mess, but that's the reality. And it's no wonder grounding and shielding, etc. are poorly understood.
> I want to know that what should be the resistance between Electronic earth & power Earth.
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There is no answer to this question. It depends on so many different possible situations that you could be asking about that it is not possible to give you a straight up answer.
I will tell you what it means in the US. It may well be different elsewhere. We use the term "ground" instead of earth. This definition is found in the NEC.
"Ground. The earth."
This is what the NEC says about the connection to earth.
"(A) Grounded Systems.
(1) Electrical System Grounding. Electrical systems that are grounded shall be connected to earth in a manner that will limit the voltage imposed by lightning, line surges, or unintentional contact with higher-voltage lines and that will stabilize the voltage to earth during normal operation."
This is the sole purpose of connecting to earth. It serves no part in clearing faults of any kind. In fact, the code specifically prohibits depending on earth to be part of the fault clearing path.
In the US this is generally via one or more of what we call grounding electrodes. In some cases the grounding electrode system (GES) consists of multiple grounding electrodes that are required to be bonded together. It is possible that the grounding electrodes may be some distance apart meaning there could be some resistance in the conductor that bonds one grounding electrode to another.
The code requires that where an electrical service or system is grounded that the bond to the earth be made in a single location.
However, if a feeder goes out to another structure, a GES is required at that structure but it has to be connected to the equipment grounding conductor (EGC).
The NEC also allows for what are called auxiliary grounding electrodes. These are required to be connected to the EGC and are not part of the GES. The most common example of this is the useless ground rod often installed at CNC machines.
That is why there is no real answer to your question.
Even thought the earth itself is a near perfect conductor, the connections to the earth (the grounding electrodes) are often not very good. In fact the code does not require any specific impedance between the grounding electrode and earth. It could be close to zero, or 1000 Ohms and it just would not matter to the code.
