It does seem that "strain" is used by some to mean series. I wish they would all uniformly use the word series.
Concerning the Hellebore you linked to, it does seem that "Brandywine™" is the trade name and the series is also "Brandywine". I also haven't been able to find what the real cultivar name for it is. But it must have a cultivar name.
The 'Dynamite' crepe myrtle is actually 'Whit II' with a trade name of Dynamite(tm). All trade name plants must have a cultivar name registered to be valid (as far as I know).