The Einstein-de Sitter model of the universe (i.e., Einstein-de Sitter universe) posits a universe 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 flat matter-only universe, i.e., at the critical density. Friedmann models (or Friedmann universes) are models of the universe adhering to the Friedmann equations, a solution to Einstein's general relativity equations. The Einstein-de Sitter model is, in effect, an approximation of modern models such as the Lambda-CDM model, and before evidence of dark energy was discovered, observation supported the Einstein-de Sitter model and it was used as a realistic model.
An earlier model, termed 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.