There may be a distinction you could draw between the use of the phrase 'social construction' that Berger and Luckmann (1966) popularized in the Social Construction of Reality, and more reflexive ideas about the constitution of social rules or 'methods' such as Garfinkel's (1967) ethnomethodology.
Berger and Luckmann's understanding of how social knowledge is accumulated and retrieved in response to the always-current need to make sense of the world draws on Alfred Schütz' concept of 'interpretative relevance', which in turn draws on what Schütz' describes as Husserl's phenomenology of time in the "passive synthesis of recognition". When we encounter some phenomenon in time, we draw on our stock of social knowledge - retrospectively - to formulate anticipations and projections to make sense of it and respond in some way. Schütz suggests that this functions as a kind of reflexive normativity - a way to synthesize subjective experience with a stock of knowledge about how things are commonly done, used, or understood. This enables us to reflect on, rationalize and stabilize our otherwise fragmentary experiences of perceptions and thoughts over time.
Garfinkel was also strongly influenced by Schütz' phenomenology, but equally strongly by Wittgenstein on rules and language games. Following Schütz', he acknowledges that social knowledge and phenomenological experience are reflexively co-constructed, but for Garfinkel this also means that the materials and objects of study for the phenomenological sociologists like Schütz are inherently unstable. Therefore following Wittgenstein, he focused on the reflexive constitution of social norms through the language-game-like 'methods' used by a social group in a way that constitutes their group-ness. His studies in 'ethnomethodology' are literally that - studies of the relatively stable methods by which members of a group constitute the relatively unstable norms, rules and phenomena of their social world.
The implications of this distinction are that while you can theorize about the social construction of gender, rationality, nationality etc. these theoretical constructs are not necessarily involved in how these abstractions are socially constituted. Conversely, in ethnomethodological studies such as conversation analysis, to claim that gender, rationality or nationality are being constituted through social interaction, analysts must be able to show that those constructs are interpretatively relevant to participants in a particular setting. So one distinction could be that describing something as 'socially constructed' presents the analyst as occupying an etic epistemological standpoint, whereas understanding how something is socially constituted might require a more emic description.