https://isabelle.systems/cookbook/src/proofs/methods/Chained_Facts.thy
talks about
We note a slight difference. In the variant with intro, a trivial goal remains that we need to solve by ‹assumption›. The reason is that ‹intro› is a ∗‹simple method› in Isabelle jargon, while ‹rule› is ∗‹proper›. Simple methods ignore chained facts and insert them into the goal state, while proper methods will usually act on them in some way.
Is there anything more to know about simple and proper methods? Especially, where can I find a list of the methods belonging to these categories?