I wouldn't be too sure they are the same. I found these postings at the Portland Nursery as if they were two different types of plants:
‘Bishop’s Children’ are seedlings of the variety ‘Bishop of Llandaff’ which retain the dark foliage of that parent, but come in a number of peony-flowered colors.
The Mystic Series: Dark foliage with red, yellow, pink and white, or orange informal decorative blooms on compact plants to about 2’ tall.
Here is a url to the mystic series. They are seriously lovely, both foliage and flowers.
http://www.mysticdahlia.com/
I thought this was an interesting quote in the Yakima Magazine.
"But life has not always been charmed for the dahlia, which has often been snubbed by more sophisticated gardeners. Perhaps it’s because influential English gardener Gertrude Jekyll commented that “the dahlia’s first duty in life is to flaunt and to swagger.” She may have had in mind “dinner plate” dahlias, which sport flowers that can be more than a foot in diameter. If their names are descriptive — “Kelvin Floodlight,” “Bodacious,” “Babylon Red” or “Gladiator” — she may have had a point. "
