We talked about this in the forum before, but I offer my opinion what sets apart isekai from the old, "otherworld" classics.
As an isekai writer myself, I think what sets the genre apart is the trope that the main character uses his/her knowledge and conveniences of the contemporary modern world (at most cases, Earth Knowledge and tech) to solve the problems he/she encounters.
For short, it answers an old question of mine from when I was a kid: "What happens when an M16 rifle and an APC are used against a dragon? And would a missile fare well against magic spells?"
Feel free to dispute or add on my take, it's only an opinion anyway.
Ok, so first off, "Isekai" is literally the Japanese word for "otherworld." I don't just mean that they have equivalent meanings. "Sekai" is the actual Japanese word for "world." The "I" prefex doesn't quite translate to English as smoothly, it doesn't have a one to one English equivalent, but "otherworld" is a prefectly valid interpretation.
Second, the term was used predating the modern era, for classics such as the famous story of Urashima Tarō who was taken to the undersea dragon palace after rescuing a sea turtle.
In regards to the story of Urashima Tarō, his story has strong parallels to some classic otherworld English fairy tales such as The King of Elfland's Daughter.
So, yeah. Isekai is literally the Japanese word for "otherworld." They have used the term literally for centuries, and the history of Isekai is also just as long as the history of Western otherworld fantasies. There really is no difference between the two.
On that subject, otherworld fantasies were actually the standard for fantasy lore up until Tolkein's The Hobbit arrived on the scene and changed all that by creating Middle Earth, which broke new ground by creating a fantasy world without introducing it through the eyes of someone from our world.
Ironically, the fad was the abandoning of the fish out of water dynamic in favor of giving us the POV of a native of the world. Now, it seems the fad is dying and proper otherworld fantasy has made a resurgence. The strange thing is that, for some reason, the west has adopted the Japanese word for otherworld and we've stopped using our own perfectly servicable native word for it.