We have messed up the terms.

We already have AGI, artificial general intelligence. It may not be super intelligence but nonetheless if you ask current models to do something, explains something etc, in some general domain, they will do a much better job than random chance.

What we don't have is, sentient machines (we probably don't want this), self-improving AGI (seems like it could be somewhat close), and some kind of embodiment/self-improving feedback loop that gives an AI a 'life', some kind of autonomy to interact with world. Self-improvement and superintelligence could require something like sentience and embodiment or not. But these are all separate issues.