The aim of the research described in this paper was to identify qualitatively different profiles of teachers' general pedagogical knowledge (GPK) as a central component of their competence. We applied a mixed Rasch model to a sample of 462 mathematics and non-mathematics teachers who were tested using a short version of the TEDS-M test for GPK. The analysis revealed two profiles that were characterized by (quantitative) differences in their overall GPK level as well as (qualitative) differences in how well these groups did on specific items. The profiles differed mainly on items dealing with adaptivity, notably on a set related to Bruner's modes of representation. A person-focused comparison of the profiles showed that teachers who had undergone training for teaching mathematics had a higher chance of belonging to the profile with strength on these and other adaptivity items. The profiles were validated against teachers' beliefs and their instructional quality. The results showed that the two groups differed significantly in their epistemological as well as teaching and learning beliefs. Moreover, they differed significantly in the cognitive activation level of their instruction.