By my reading, the original PBL model has a clearly staged process with a focus on declarative knowledge, which is then usually assessed by means of individual examination (see the Aalborg model for example). The pedagogy is also well-documented, with both teacher approach and types of interaction preset within a schedule of engagement. Studio-based learning I would argue does not share these characteristics. While there may be stages, they tend to iterate and are perhaps less formalised (if we view this across the design disciplines). Certainly the pedagogy is less well documented. Project-based learning, with its looser definition, compares more readily - similar to PBL, there is a problem situation, definition, exploration and iteration, and a theoretical preference for guided learning, rather than didactic teaching. The major difference is that project based learning is focused on the development of an artefact, as is its assessment.
For further reading I'd suggest Kilpatrick (1918) and Adderley et al (1975) on project based learning, and Boud & Felitti (1997) on problem based learning, especially the chapter by Engel. You are right in your analysis that there is little in the field on design education - there are one or two empirical studies on aspects of the process (eg Blair 2006). Curriculum is more troublesome and sorely in need of research to take us beyond didactics.