Covariant and contravariant indices would be the formal terms. I'm not really sure whether I've seen "upstairs" written down. Sub/superscript... strike me as t

Covariant and contravariant indices would be the formal terms. I'm not really sure whether I've seen "upstairs" written down. Sub/superscript... strike me as the typographical terms, not the meaning? Like $x_\mathrm{alice}$ is certainly a subscript, and footnote 2 is a superscript, but neither is an index.