Enterprise Architecture Framework is a set of assumptions, concepts, values, and practices that constitutes a way of looking at enterprise reality via views on (architecture) models. It offers a fundamental structure, serving as a scaffold for developing, maintaining, and using EA.
Zachman visualises the entire enterprise at one glance. All aspects are treated as equally important; should be described as simple, basic model.
The Open Group Architecture Framework (TOGAF) is a generic yet comprehensive methodological framework for developing enterprise architecture.
TOGAF Architecture Development Methodology (ADM)
TOGAF Architecture Content Framework
TOGAF Architecture Capability Framework
Gartner Methodology essentially stems from the META Group. It does not publish a formal framework or a process to do EA. Instead, its consultants guide enterprises in setting up a process by which EA can emerge from their business strategy.
Source: Stefan Bente et. al., Collaborative Enterprise Architecture, Morgan Kaufmann, Elsevier 2012. ISBN 9780124159341.