The Einstein-de Sitter model of the universe (i.e., Einstein-de Sitter universe) posits it is constrained by gravity according to general relativity, and expanding just enough that it will continue expanding to infinity, and no more than that. (Analogous is a rocket launched at exactly escape velocity and no more.) It is a particular Friedmann model for a particularly flat matter-only universe. Friedmann models (or Friedman universes) are models of the universe adhering to the Friedman equations, a solution to Einstein's general relativity equations, and are, in effect, approximations of modern models like the Lambda-CDM model.
An earlier model, a de Sitter universe, represents a theoretical universe simplified in that the effects of matter are ignored. It showed expansion of the universe and was early among models that did so.