Physicists often refer to spaces in supergeometry, such as supermanifolds or super schemes, as superspaces, regardless the formalism. Hence a superspace can be an affine superspace (the affine counterpart of the supervector space over real or complex numbers), superscheme, supermanifold (of either Leites or de Witt kind) etc.
I. L. Buchbinder, S. M. Kuzenko, Ideas and methods of supersymmetry and supergravity; or A walk through superspace
S.J. Gates Jr, M.T. Grisaru, M. Rocek, W. Siegel, Superspace, or One thousand and one lessons in supersymmetry textbook (1983), available as arXiv:hep-th/0108200