Coalition Logic is an important logic in logical research on strategic reasoning. In two recent papers, Li and Ju argued that generally, concurrent game models, models of Coalition Logic, have three too strong assumptions: seriality, independence of agents, and determinism. They presented eight coalition logics based on eight classes of general concurrent game models, determined by which of the three assumptions are met. In this paper, we show that each of the eight logics is also determined by four other kinds of models, with respective properties, that is, single-coalition-first action models, single-coalition-first neighborhood models, tree-like grand-coalition-first action models, and tree-like single-coalition-first neighborhood models.