What is the concrete type for this IEnumerable<string>?
private IEnumerable<string> GetIEnumerable()
{
    yield return "a";
    yield return "a";
    yield return "a";
}
What is the concrete type for this IEnumerable<string>?
private IEnumerable<string> GetIEnumerable()
{
    yield return "a";
    yield return "a";
    yield return "a";
}
It's a compiler-generated type. The compiler generates an IEnumerator<string> implementation that returns three "a" values and an IEnumerable<string> skeleton class that provides one of these in its GetEnumerator method.
The generated code looks something like this*:
// No idea what the naming convention for the generated class is --
// this is really just a shot in the dark.
class GetIEnumerable_Enumerator : IEnumerator<string>
{
    int _state;
    string _current;
    public bool MoveNext()
    {
        switch (_state++)
        {
            case 0:
                _current = "a";
                break;
            case 1:
                _current = "a";
                break;
            case 2:
                _current = "a";
                break;
            default:
                return false;
        }
        return true;
    }
    public string Current
    {
        get { return _current; }
    }
    object IEnumerator.Current
    {
        get { return Current; }
    }
    void IEnumerator.Reset()
    {
        // not sure about this one -- never really tried it...
        // I'll just guess
        _state = 0;
        _current = null;
    }
}
class GetIEnumerable_Enumerable : IEnumerable<string>
{
    public IEnumerator<string> GetEnumerator()
    {
        return new GetIEnumerable_Enumerator();
    }
    IEnumerator IEnumerable.GetEnumerator()
    {
        return GetEnumerator();
    }
}
Or maybe, as SLaks says in his answer, the two implementations end up in the same class. I wrote this based on my choppy memory of generated code I'd looked at before; really, one class would suffice, as there's no reason the above functionality requires two.
In fact, come to think of it, the two implementations really should fall within a single class, as I just remembered the functions that use yield statements must have a return type of either IEnumerable<T> or IEnumerator<T>.
Anyway, I'll let you perform the code corrections to what I posted mentally.
*This is purely for illustration purposes; I make no claim as to its real accuracy. It's only to demonstrate in a general way how the compiler does what it does, based on the evidence I've seen in my own investigations.
The compiler will automatically generate a class that implements both IEnumerable<T> and IEnumerator<T> (in the same class).
The concrete implementation of IEnumerable<string> returned by the method is an anonymous type generated by the compiler
Console.WriteLine(GetIEnumerable().GetType());
Prints :
YourClass+<GetIEnumerable>d__0