Definition of Bessel/Fourier-Jacobi/Whittaker models

Question

I've seen the notion of the models in the title a lot in the context of automorphic forms and representations, but I wonder if there's any nice reference for the definition of them for general reductive groups, with some motivations for their namings. I'm pretty sure that the name Whittaker model comes from the Whittaker functions that give Fourier-like expansion of Maass wave forms, and somehow generalize the notion of Fourier coefficients for the general automorphic forms. But I have no idea with the rest of them, although I've seen the definition of them for some classical groups in many papers, especially related to Gan-Gross-Prasad conjectures. My naive guess is that Bessel model should be motivated from the classical Bessel functions but don't know how. Also the name Jacobi in Fourier-Jacobi may come from theta functions, since all the Fourier-Jacobin periods I've seen are defined in terms of Weil representations and theta functions.