The sientific name includes the Greek word "ortho" (which means "straight").
This refers to the style of the stem.
The word "secunda" means "side-flowering",
i.e., flowers are on one side of the flowering stem.
One sided pyrola is a perennial with single to several erect stems arising from a rootstocks.
By looking closely, you can see that the pedicels of this plant in
fact arise on all sides of the stem, but they all turn to one side of the stem.
One-sided pyrola is believed to be extinct in Connecticut.
(from Connecticut Botanical Society)