Why is a borrowed range not an iterator, but the range is?

To understand what is happening here it is helpful to understand how for loops work in Rust.

Basically a for loop is a short hand for using an iterator, so:

for item in some_value {
    // ...
}

is basically a short-hand for

let mut iterator = some_value.into_iter();
while let Some(item) = iterator.next() {
    // ... body of for loop here
}

So we can see that whatever we loop over with the for loop, Rust calls the into_iter method from the IntoIterator trait on. The IntoIterator trait looks (approximately) like this:

trait IntoIterator {
    // ...
    type IntoIter;
    fn into_iter(self) -> Self::IntoIter;
}

So into_iter takes self by value and returns Self::IntoIter which is the type of the iterator. As Rust moves any arguments which are taken by value, the thing .into_iter() was called on is no longer available after the call (or after the for loop). That's why you can't use coll in your first code snippet.

So far so good, but why can we still use a collection if we loop over a reference of it as in the following?

for i in &collection {
    // ...
}
// can still use collection here ...

The reason is that for a lot of collections C, the IntoIterator trait is implemented not just for the collection, but also for a shared reference to the collection &C and this implementation produces shared items. (Sometimes it is also implemented for mutable references &mut C which produces mutable references to items).

Now coming back to the example with the Range we can check how it implements IntoIterator.

Looking at the reference docs for Range, Range strangely does not seem to implement IntoIterator directly... but if we check the Blanket Implementations section on doc.rust-lang.org, we can see that every iterator implements the IntoIterator trait (trivially, by just returning itself):

impl<I> IntoIterator for I
where
    I: Iterator

How does this help? Well, checking further up (under trait implementations) we see that Range does implement Iterator:

impl<A> Iterator for Range<A>
where
    A: Step, 

And thus Range does implement IntoIterator via the indirection of Iterator. However, there is no implementation of either Iterator for &Range<A> (this would be impossible) or of IntoIterator for &Range<A>. Therefore, we can use a for loop by passing Range by value, but not by reference.

Why can &Range not implement Iterator? An iterator needs to keep track of "where it is", which requires some kind of mutation, but we cannot mutate a &Range because we only have a shared reference. So this cannot work. (Note that &mut Range can and does implement Iterator - more on this later).

It would technically be possible to implement IntoIterator for &Range as that could produce a new iterator. But the likelihood that this would clash with the blanket iterator implementation of Range would be very high and things would be even more confusing. Besides, a Range is at most two integers and copying this is very cheap, so there is really no big value in implementing IntoIterator for &Range.

If you still want to use collection, you can clone it

for i in coll.clone() { /* ... */ }
// `coll` still available as the for loop used the clone

This brings up another question: If we can clone the range and it is (as claimed above) cheap to copy it, why doesn't Range implement the Copy trait? Then the .into_iter() call would copy the range coll (instead of moving it) and it could still be used after the loop. According to this PR the Copy trait implementation actually existed but was removed because the following was considered a footgun (hat tip to Michael Anderson for pointing this out):

let mut iter = 1..10;
for i in iter {
    if i > 2 { break; }
}
// This doesn't work now, but if `Range` implemented copy,
// it would produce `[1,2,3,4,5,6,7,8,9]` instead of 
// `[4,5,6,7,8,9]` as might have been expected
let v: Vec<_> = iter.collect();

Also note that &mut Range does implement iterator, so you can do

let mut iter = 1..10;
for i in &mut iter {
    if i > 2 { break; }
}
// `[4,5,6,7,8,9]` as expected
let v: Vec<_> = iter.collect();

Finally, for completeness, it might be instructive to see which methods are actually called when we loop over a Range:

for item in 1..10 { /* ... */ }

is translated to

let mut iter = 1..10.into_iter();
//                   ˆˆˆˆˆˆˆˆˆ--- which into_iter() is this?
while let Some(item) = iter.next() { /* ... */ }

we can make this explicit using qualified method syntax:

let mut iter = std::iter::Iterator::into_iter(1..10);
// it's `Iterator`s  method!  ------^^^^^^^^^
while let Some(item) = iter.next() { /* ... */ }