I agree they are not the same Garden. It is believed "Eden the Garden of God" was on this earth before Adam and Eve and Satan ruled the earth, having been given dominion over the earth. How long before Adam and Eve we don't know. When he rebelled against God we don't know.
It seems that God took the dominion of this earth from Satan when he fell and later gave it to man. The gap in time is unknown.
Gen 2:10; Now
a river flowed out of Eden to water the garden; and from there it divided and became four rivers.
Gen 2:11; The name of the first is
Pishon; it flows around the whole land of Havilah, where there is gold.
Gen 2:12; The gold of that land is good; the bdellium and the onyx stone are there.
Gen 2:13; The name of the second river is
Gihon; it flows around the whole land of Cush.
Gen 2:14; The name of the third river is
Tigris; it flows east of Assyria. And the fourth river is the
Euphrates.
Gen 2:15; Then the LORD God took the man and put him into the garden of Eden to cultivate it and keep it.
We know where two of these rivers are even today. They dump into the Persian Gulf. The Gihon and Pishon are unknown, are perhaps re-named.
As far as Satan falling in the "gap theory". There is yet another option. We don't know how long Adam and Eve were on the Earth before they sinned, it could have been decades.
Yet another theory says Adam and Eve didn't start aging until they sinned. So, they could have been on the Earth thousands of years.
Gen 5:2; He created them male and female, and He blessed them and named them Man in the day when they were created.
Gen 5:3;
When Adam had lived one hundred and thirty years, he became the father of a son in his own likeness, according to his image, and named him Seth.
Gen 5:4; Then the days of Adam after he became the father of Seth were eight hundred years, and he had other sons and daughters.
Gen 5:5; So
all the days that Adam lived were nine hundred and thirty years, and he died.
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Rev 12:7; And
there was war in heaven, Michael and his angels waging war with the dragon. The dragon and his angels waged war,
Rev 12:8; and they were not strong enough, and
there was no longer a place found for them in heaven.
Rev 12:9; And
the great dragon was thrown down, the serpent of old who is called the devil and Satan, who deceives the whole world; he was thrown down to the earth, and his angels were thrown down with him.
Luke 10:18; And He said to them, "
I was watching Satan fall from heaven like lightning.
How long did this war in heaven last? Eventually Satan and his angels were overcome, Satan was cast out of heaven, but apparently was still allowed to visit from time to time.
Job 1:6; Now there was a day when the sons of God came to present themselves before the LORD, and Satan also came among them.
Job 1:7; The LORD said to Satan, "From where do you come?" Then Satan answered the LORD and said, "From roaming about on the earth and walking around on it."
Yet another theory says Job was alive when Adam was still alive. Perhaps Satan wasn't kicked out of heaven yet.