Is it reincarnation if...?

Ive always thought of reincarnation is used in a similar way as yellow, its not bright yellow with a tiny bit of pink.
Reincarnation is used as a umbrella to cover all similar types.
Language is not designed its organically grown and like waters follow trends and is highly illogical.

But yes technically many of the stories tagged reincarnation is inaccurate, transmigration would likely be a better tag if more knew the word.
Remember reading a novel called transmigration of eldritch palmer couple of years ago and after i was finished still didnt know what the hell the word "transmigration" meant. Think lot of people like me simply dont know what it means unless they happen to come across a rare situation that leads you to learning the word.