Recursion reduces each step toward a base case: each step is defined in terms of previous/simpler steps, not more advanced ones. The "recursive" in "recursive self improvement" has things precisely backward. Iteration correctly describes a process where each step is the starting point of its successive step, so it should be "iterative self improvement" but I guess that didn't sound as cool.

I think you’re conflating the direction of definition with the direction of evaluation.

Compare the similarity of:

  AI(n) = improve(AI(n-1))

With:

  Fib(n) = Fib(n-1) + Fib(n-2)

The latter is a classic example of recursion. So why isn’t the former?

Edit: formatting

I think you're confusing a recurrence relationship with recursive execution. Until AI has control over its inputs (including physical inputs - compute hardware, etc.) it's not quite RSI. We'll get there. They'll get there, rather.

It's not a nuance, it's a sequence.