Bayes' theorem and Bayes' rule are essentially the same equation. Most people will use the two interchangeably. Bayesianism is a perspective on how to do model

Bayes' theorem and Bayes' rule are essentially the same equation. Most people will use the two interchangeably. Bayesianism is a perspective on how to do modelling under uncertainty. It doesn't reduce to "use Bayes' theorem", even though all Bayesian inference will do that in some fashion.