What is the relation between Iterable and Iterator?

In short: An Iterator does have state, whereas an Iterable does not.

See the API docs for both.

Iterable:

A base trait for iterable collections.

This is a base trait for all Scala collections that define an iterator
method to step through one-by-one the collection’s elements.
[…] This trait implements Iterable’s foreach method by stepping
through all elements using iterator.

Iterator:

Iterators are data structures that allow to iterate over a sequence of
elements. They have a hasNext method for checking if there is a next
element available, and a next method which returns the next element
and discards it from the iterator.

An iterator is mutable: most operations on it change its state. While
it is often used to iterate through the elements of a collection, it
can also be used without being backed by any collection (see
constructors on the companion object).

With an Iterator you can stop an iteration and continue it later if you want. If you try to do this with an Iterable it will begin from the head again:

scala> val iterable: Iterable[Int] = 1 to 4
iterable: Iterable[Int] = Range(1, 2, 3, 4)

scala> iterable.take(2)
res8: Iterable[Int] = Range(1, 2)

scala> iterable.take(2)
res9: Iterable[Int] = Range(1, 2)

scala> val iterator = iterable.iterator
iterator: Iterator[Int] = non-empty iterator

scala> if (iterator.hasNext) iterator.next
res23: AnyVal = 1

scala> if (iterator.hasNext) iterator.next
res24: AnyVal = 2

scala> if (iterator.hasNext) iterator.next
res25: AnyVal = 3

scala> if (iterator.hasNext) iterator.next
res26: AnyVal = 4

scala> if (iterator.hasNext) iterator.next
res27: AnyVal = ()

Note, that I didn’t use take on Iterator. The reason for this is that it is tricky to use. hasNext and next are the only two methods that are guaranteed to work as expected on Iterator. See the Scaladoc again:

It is of particular importance to note that, unless stated otherwise,
one should never use an iterator after calling a method on it. The two
most important exceptions are also the sole abstract methods: next and
hasNext.

Both these methods can be called any number of times without having to
discard the iterator. Note that even hasNext may cause mutation —
such as when iterating from an input stream, where it will block until
the stream is closed or some input becomes available.

Consider this example for safe and unsafe use:

def f[A](it: Iterator[A]) = {
  if (it.hasNext) {            // Safe to reuse "it" after "hasNext"
    it.next                    // Safe to reuse "it" after "next"
    val remainder = it.drop(2) // it is *not* safe to use "it" again after this line!
    remainder.take(2)          // it is *not* safe to use "remainder" after this line!
  } else it
}

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