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That sounds more iterative than recursive.

Recursion requires feeding the output back into the input, so creating version 4 requires results from version 3. You cannot recur in parallel.

Iteration does not. You can iterate in parallel.

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You can search in parallel, but a depth N search can only become a depth N+1 search after the depth N is done (i.e. sequentially).

In any case the name RSI has stuck - the idea doesn't change or make any more sense by giving it a different name.

Because "depth" is recursive.

You can search twice without waiting for the results of your first search: iteration.

You can't if the thing you need to search for is the results of your first search: recursion.

Here's the concept.

Version 1 -> Version 2 -> Version 3 -> ...

You can call it krispy kreme donuts if you want to.

The “recursive” part comes from the fact that you have an AI which was developed by an AI (that was developed by an AI (that was developed by an AI (…)))

Sounds like "recursively" walking to the grocery store by putting one foot in front of the other (that put itself in front of the other (that put itself in front of the other (...)))

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