Critical realist or realist?

Having pondered my methodological approach, supervisors are happier with this second attempt at the chapter. I've written:

A reason this research should use a constructivist approach is that project participants construct each other’s behaviours in the context of a project and shape each other’s understanding. Examples of this approach discussed in the literature review include Schein (Schein, 1997), Bovens’ (Bovens, 2007) constructions of client models, Wenger’s communities of practice (Wenger, 1998), the importance of space and time for understanding projects (Maaninen-Olsson & Müllern, 2009). However, this research takes a critical realist research perspective because, although organisations’ IS projects take place in real objective spaces, each individual participant constructs themselves in a particular way in relation to the project setting.

Supervisor #1 says that I should say it's a realist perspective, not a critical realist perspective. I'm not sure about this because I thought there was a difference that mattered, and isn't realism close to positivism? Or does the term 'critical' apply when research seeks to identify practices or structures in order to highlight inequalities or injustices, in which case, I should remove it, because I'm not attempting to highlight such inequalities. If I remove the word, then everything else I've written still holds, but if I leave it in, then I'm open to queries about my perspective.

I'll ponder.