the genre your reffering to is called isekai
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Well, as far as I know "isekai" is not technically a recognized or accepted genre but fantasy. Although when it started to become very popular, especially in Asia, people started to refer to it as it's own genre. Since one of my new collections is called Isekai – FVN, I too, see it as it's own established genre. ("Isekai" actually just means "different world" in Japanese)