Environmental Impact Statement: Detailed written statement required by section 102(2)(C) of NEPA for a proposed major Federal action significantly affecting the quality of the human environment. (From Energy.gov Office of NEPA Policy and Compliance)
Environmental Assessment: Concise public document that a Federal agency prepares under NEPA to provide sufficient evidence and analysis to determine whether a proposed agency action would require preparation of an environmental impact statement or a finding of no significant impact. (From Energy.gov Office of NEPA Policy and Compliance)
DEIS = Draft Environmental Impact Statement
EIS = Environmental Impact Statement
NEPA = National Environmental Policy Act
NEPA requirements go into effect when airports, buildings, military complexes, highways, parkland purchases and other federal activities with the potential for impacts are proposed. Environmental assessments (EA's) and Environmental Impact Statements (EIS's), which are assessments of the likelihood of impacts from alternative courses of action, are required from all federal agencies and are the most visible NEPA requirements.
NEPA establishes the requirement that all federal agencies' funding or permitting decisions be made with full consideration of the impact to the natural and human environment. And it requires agencies disclose these impacts to interested parties and the general public. The central element in the environmental review process is a rigorous evaluation of alternatives including the "no action" alternative.
text from: http://www.epa.gov/region1/nepa/