What's the difference between "act" and "action"? More specifically in the way they are generally used (and not more specific theatrical definitions, for instance)?
This is actually a question to study with a dictionary.
Act is defined by Dictionary.com as:
(Note that I removed the legal, theatrical, and philosophical definitions in the above.)
Action is defined as:
(Here I removed the physiological, literature-related, theatrical, fine arts-related, legal, slang, and ecclesiastical definitions.) I know this is a lot to take in, but once you peruse the two entries, you get a pretty good idea of the usage differences as well as the meaning differences.
I'd suggest that a difference between definition 2 of action and the definition of act is that actions are almost always fundamental acts (e.g. moving your arm), while acts can be larger, and made up of many smaller actions (e.g. robbing a bank). There is, of course, a lot of grey area in between the definitions where they overlap, so that's not comprehensive. Sometimes either works just as well as the other.
Other than definition 2 (and possibly 3) of action, act and action seem pretty well defined relative to one another.
I had said in the unedited version of this post that one of the main differences was that act tends to describe abstract events and that action tends to describe concrete ones. I’ll modify that and say that action perhaps describes a more dynamic event than act. We might speak of an act of folly, but rarely of an action of folly. On the other hand, we might say the action of the piston causes the rotor to turn, but never, surely, the act of the piston causes the rotor to turn. Structurally, action can be uncountable, as in The government must take immediate action. Act never can. We might conceivably speak of An action such as that can never be forgiven, but never *Act such as that can never be forgiven.
As I said earlier, it's a big question to answer fully in a few lines, and without further research. Others, presumably, think the same, given the absence any other answer.