Online learning is the term, yes.

> The way “recursive self-improvement” is being used recently seems to be intentional marketing. A model helping code/train/test the next generation of its model family isn’t technically “self”-improvement.

The term RSI is ~20 years old at this point, and the concept is even older. If an AI can't continuously modify itself and instead has to build a successor that builds a successor, that changes some specifics (for example, the alignment problem becomes more relevant - how can the AI ensure that its successor shares its goals?) but it's still a situation that may produce exponential growth, and hence most RSI-related considerations still apply.

(In fact, as a toy example, note that it's in theory possible to get exponential growth in capabilities even if you hold the software fixed, if e.g. you have an AI that can design and build better hardware to run itself faster on, which lets it design even better hardware even faster.)