This chapter aims to present and discuss concepts that help researchers to characterise a class as a group. We selected the concepts of didactic contract and milieu in the framework of the Joint Action Theory in Didactics (JATD) that is related to theory of didactic situation. We present examples of how to use these concepts to analyse two classroom situations designed to introduce the dynamics section of a mechanics sequence at grade 10 level. These examples illustrate different contracts, e.g. in one class the teacher expects the students to give reasons for their proposal, whereas in the other class the teacher expects a right answer to develop knowledge; thus, there are different statuses of knowledge. Then we introduce the concepts of the models of identity and normative identity which also characterise the class in the framework of sociocultural theories. All these concepts share the perspective of characterising the class as a group and of taking into account the contingency of these concepts. The didactic contract and normative identity or model of identity are specific to classroom situations and evolve in the classroom with time. Among the differences, we note the historical evolution of the didactic contract that emerged in 1978, whereas the normative identity/model of identity is much more recent and related to a focus of the sociocultural theory on social structure and not mainly on personality and interactions. This analysis of concepts of different theoretical frameworks strives on the one hand to promote a better understanding between researchers in our international community and on the other hand to develop investigation into classroom practices which allow the design of resources for teacher education and science teaching.