Solution 1:

The documentation on MSDN is disappointing, but decompiling Task.Delay using Reflector gives more information:

public static Task Delay(int millisecondsDelay, CancellationToken cancellationToken)
{
    if (millisecondsDelay < -1)
    {
        throw new ArgumentOutOfRangeException("millisecondsDelay", Environment.GetResourceString("Task_Delay_InvalidMillisecondsDelay"));
    }
    if (cancellationToken.IsCancellationRequested)
    {
        return FromCancellation(cancellationToken);
    }
    if (millisecondsDelay == 0)
    {
        return CompletedTask;
    }
    DelayPromise state = new DelayPromise(cancellationToken);
    if (cancellationToken.CanBeCanceled)
    {
        state.Registration = cancellationToken.InternalRegisterWithoutEC(delegate (object state) {
            ((DelayPromise) state).Complete();
        }, state);
    }
    if (millisecondsDelay != -1)
    {
        state.Timer = new Timer(delegate (object state) {
            ((DelayPromise) state).Complete();
        }, state, millisecondsDelay, -1);
        state.Timer.KeepRootedWhileScheduled();
    }
    return state;
}

Basically, this method is just a timer wrapped inside of a task. So yes, you can say it's just like timer.