Actions are Events
This can't be any more explicit than what is stated in the Redux documentation.
Actions describe the fact that something happened
http://redux.js.org/docs/basics/Reducers.html
Action Creators are Commands... and Their Handlers
The command and the command handler are squashed into the same concept. The "command" doesn't travel outside the application, so there's less need to convert it to a distinct command message. In fact, doing so feels awkward and redundant due to the next point.
An event (aka action) is almost always generated by a handler. One of the main reasons commands can fail on the back-end is because they are not trusted, so the code inside the handler must validate the command (aka protect invariants). On the front end, the command is considered trusted because the components + state are protecting the invariants. For example, you won't be able to issue a command (the button will be disabled) if the invariant is violated. (If you can, it's considered a bug.)
There's also how errors are handled. They are typically considered events on the UI (user needs to be notified), whereas command handlers typically just return errors as responses without affecting the domain.
What remains the same about the command handler between front- and back-ends is that the handler manages dependencies for the use case. On the front end that often takes the form of wrangling HTTP API calls.
Store is a View Database, Reducers are View Updaters
This is evident from the note on Reducers.
As your app grows, instead of adding stores, you split the root reducer into smaller reducers independently operating on the different parts of the state tree.
http://redux.js.org/docs/api/Store.html in A Note for Flux UsersEssentially, different properties off of the Store's state represent different views. A reducer is responsible for updating its own view.
But keep in mind...
I'm just getting started with React/Redux. These are mental models based on an understanding of CQRS/ES. "All models are wrong. Some of them are useful." (George E. P. Box) This doesn't map all the odds and ends from CQRS/ES and friends, but hopefully it's useful to you.