ILookup<TKey, TVal> vs. IGrouping<TKey, TVal>

I've been having trouble articulating the differences between ILookup<TKey, TVal> and IGrouping<TKey, TVal>, and am curious if I understand it correctly now. LINQ compounded the issue by producing sequences of IGrouping items while also giving me a ToLookup extension method. So it felt like they were the same until I looked more closely.

var q1 = 
    from n in N
    group n by n.MyKey into g
    select g;
// q1 is IEnumerable<IGrouping<TKey, TVal>>

Which is equivalent to:

var q2 = N.GroupBy(n => n.MyKey, n => n);
// q2 is IEnumerable<IGrouping<TKey, TVal>>

Which looks a lot like:

var q3 = N.ToLookup(n => n.MyKey, n => n);
// q3 is ILookup<TKey, TVal>

Am I correct in the following analogies?

1. An IGrouping<TKey, TVal> is a single group (i.e. a keyed sequence), analogous to KeyValuePair<TKey, TVal> where the value is actually a sequence of elements (rather than a single element)
2. An IEnumerable<IGrouping<TKey, TVal>> is a sequence of those (similar to what you get when iterating over an IDictionary<TKey, TVal>
3. An ILookup<TKey, TVal> is more like a IDictionary<TKey, TVal> where the value is actually a sequence of elements