Sorry been a bit hectic, being active on and off and missed this wonderful question in the process.
Thanks also @KMac for bringing this into my attention.
I’ll be honest I heard abt contradictions on these minor details, this is one that I skimmed past before, but I remembered about it actually talking about a general region in the original language. It cannot be read literally as some translation did, as if it is homing in on a specific city.
The Verses in Question:
chōran tōn Gerasēnōn (region of Gerasenes)
chōran tōn Gerasēnōn (region of Gerasenes)
chōran tōn Gadarēnōn (region of Gadarenes)
Region of Gadara and Gerasa
And Gadara and Gerasa are names of specific cities like you mention, but they both fall in the same province/regent/state-equivalent, called Decapolis. So does the Sea of Galilee. Meaning, to say Jesus go to either the REGION of Gadarenes or Gerasenes is actually geographically not inaccurate, and acceptable during those times as a literary style.
Different Set of Audience
The reason for their not being specific city-wise is because they have a different set of audience. Mark and Luke are generally known to be writing to a more Gentile audience, which are more familiar with Gerasenes. It is supposed to be a more well-known city to non-locals.
Matthew’s audience however is geared towards the Jews, who are more familiar with the capital city of Decapolis province, which is Gadarenes.
Example: Where I Am From
It will be like if I were to explain to you where I am from. Just to let you know upfront, the country is Indonesia, the island is Java island, the province DKI Jakarta, and the city is North Jakarta, and my town is Tanjung Priok, my area is Sunter.
To a foreigner, I would say I’m from the country of Bali. (Because people might not know Indonesia, but everyone knows Bali LOL)
To a fellow Indonesian, I would say Jakarta.
To a Jakartan, I would tell them North Jakarta.
To a North Jakartan, I would say Sunter. Super specific, because they would understand. I hope that makes sense.
Understanding Literary Style
In this age, we are into specifics. Back then the writing style was quite different, they try to relate to their audience with a more familiar area to identify with, usually from a wider scope of region. So it was not wrong, but it was not specifically precise, because they were not trying to. People in those times would know, just like you would know I’m not from Bali of Indonesia, but I’m from Indonesia where Bali is. If it was an error, they would be easily refuted by the people during those days when they circulate these synoptic gospel documents. But the critics didn’t start until recently during our time, but the people back then had no problem understanding Mark, Luke and Matthew.
Where Was Jesus Then?
Just to be sure where Jesus was specifically, you are probably right, He was probably in the town of Gergesa, otherwise known as Kursi, which is situated on the bank of the Sea of Galilee, and still within the province of Decapolis, where Gadara and Gerasa belonged also.
So some scholars did debate that those cities could be just spelling variants of Gergesa, which is not uncommon to ancient manuscripts. It is more like the way we spell the country Brazil which is the english spelling, the locals and Spanish known it as Brasil, Brasilien in German, Brasile in Italian, Brésil in French.
Imagine during those days, you have so many cross settlers, foreign people from all around the world, as it was one of the major hub in the ancient eastern world. The city namings were not as technically unified and decided like today. I’m not saying there wasn’t at all. But there were lot of variants known to different people.
Remember, even if it is not due to spelling variant, it is still not inaccurate and shouldn’t be considered a geographical error.
Sorry, I kept rambling. It is 11:40pm now writing this in the dark, on mobile with my wife asleep beside me, was just back at 10:30pm after a very eventful day. Forgive me if in case I’m not being too coherent with laying out my points. Feel free for the more knowledgable to correct any mistakes, add anything I might have missed or revise certain points.
Hope it helps though, I learnt as much as you did refreshing this topic for myself.
Blessings in Christ,