The term grammatical relation is the most common term in American linguistics for notions such as 'subject', object', etc. (e.g. Marantz 1984 and the Relational Grammar literature)
The term is used to refer to a link between two elements, while grammatical function refers to one of the members of a relation.
Marantz, Alec P. 1984. On the nature of grammatical relations. Cambridge, MA: MIT Press.