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.