> That is, since generators are primarily used to simplify the writing of iterators, the yield statement in a generator does not specify a coroutine to jump to, but rather passes a value back to a parent routine.

Another term for this asymmetric coroutine, as opposed to symmetric coroutine. Coroutines in Lua are asymmetric, but they're not generally referred to as generators as they're much more capable than what are called generators in other languages, like Python. This is largely because Lua's coroutines are stackful rather than stackless, which is an orthogonal, more pertinent dimension when implementing concurrency frameworks.

You can implement symmetric coroutines using asymmetric coroutines, and vice versa, by implementing a higher-level library that implements one using the other. So in principle they have equivalent expressive power, formally speaking. Ultimately the distinction between these terms, including generator, comes down to implementation details and your objective. And just because a language name-drops one of these terms doesn't mean what they provide will be as useful or convenient in practice as a similarly named feature in another language. Other dimensions--stack semantics, type system integration, etc--can easily prove the determining factor in how useful they are.