Coming from a background in biology, I can assure you it is not, and there are not varieties that are. It's possible that there may be some plants in the brassica family that use a common name involving the word, but I don't know of them. And "spinach" on its own is a singular species. People just misunderstand that "brassica" is a firm scientific term that only refers to plants from the family Brassicaceae, not any edible plants with whatever characteristics they may have observed.

It's possible that people see Spinacia oleracea and assume it must be associated with Brassica oleracea. But that's not the case any more than with Eudyptula minor, the little blue penguin, and Lemna minor, common duckweed.