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In my understanding AI is an even broader term and means "any solution that imitates intelligent behavior". E.g. expert systems which are pretty much a bunch of if-then rules are also considered AI.

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It's my understanding as well, many things that a modern programmer thinks in term of "computation" were once considered to be "AI". Lisp and Prolog were "AI", even the A* algorithm is still considered a rudimentary form of "AI" in textbooks just because it uses heuristics. There's a joke that says "every time AI researchers figure out a piece of it, it stops being AI" [0].

It's why I use "AI" and "ML" interchangeably although I know it's technically incorrect - the formal definition doesn't match what people are currently thinking.

[0] https://en.wikipedia.org/wiki/AI_effect

There have traditionally been different approaches and definitions for AI. Some emphasize behaviour while others emphasize the logic behind the behaviour. (In some sense, while expert systems of course were an attempt at getting practical results, they might also have been an attempt to implement what was seen as human reasoning, while e.g. black box machine learning could be more about just getting the behaviour we want.) Some approaches view agents as intelligent if their action resembles humans or other beings that we consider intelligent, while other approaches are merely interested in whether they perform well at a specified task, perhaps more so than humans.

So yes, "any solution that imitates intelligent behaviour" is probably right, but with nuances with regard to what that actually means.

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