It's confusing because Larkspur is a common name. I know larkspur as the annual - delphinium consolida. The one in your picture is delphinium elatum. They're both delphiniums but different species. The larkspur (or d.consolida) has smaller more delicate flowers. They're a hardy annual but will re-seed. If you grow the two side by side there's a big difference.
LOL! She means that the genus name has been changed for larkspur from delphinium to consolida. It happens a lot - just to confuse us. Baa - I thought it was the other way around tho ... I thought it was consolida but changed now to delphinium? Either way Mimi - delphinium consolida & consolida ajacis are the same plant [synonyms of each other]... the annual larkspur.