1. A doctrine whose source is authority (usually but not always a deity) rather than observation and
2. Rituals based on that doctrine
One might argue that the actual human practice of science sometimes involves the acceptance of authoritative doctrine (e.g. peer-reviewed papers) and associated rituals (e.g. conferences), but that is not quite true because the rituals are not based on the doctrine. Scientific conferences are not held because there is a peer-reviewed paper that says that they should be, they are held because empirically they help to advance the scientific process (or at least did in the past). Religious rituals exist entirely because of authoritative doctrine. There is no reason for (say) communion or baptism other than what is written in the Bible or proclaimed by the church.
> science similarly includes a lot of areas where our predictions are not "extraordinarily accurate"
Sure. Science isn't perfect. The view it provides us into the future isn't flawless, it's just vastly better than anything else humans have ever tried.
The fact that I recognize there are both faith and religious elements to science only makes it easier to explain how and why science is better than religion.
Note that science similarly includes a lot of areas where our predictions are not "extraordinarily accurate" (all the statistics-based science, like medicine, social sciences...) in any particular case, yet it's still science because we recognize the limits (eg. "with a large number of samples, this will mostly happen").